{"id":549161,"date":"2021-10-20T05:53:30","date_gmt":"2021-10-20T05:53:30","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=549161"},"modified":"2021-10-28T08:13:09","modified_gmt":"2021-10-28T08:13:09","slug":"rs-aggarwal-solutions-for-class-9-maths-chapter-2-polynomials","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rs-aggarwal-solutions-for-class-9-maths-chapter-2-polynomials\/","title":{"rendered":"RS Aggarwal Solutions for Class 9 Maths Chapter 2\u2013Polynomials"},"content":{"rendered":"\n

Class 9: Maths Chapter 2 solutions. Complete Class 9 Maths Chapter 2 Notes.<\/p>\n\n\n\n

RS Aggarwal Solutions for Class 10 Maths Chapter 2\u2013Polynomials<\/h2>\n\n\n\n

RS Aggarwal 9th Maths Chapter 2, Class 9 Maths Chapter 2 solutions<\/p>\n\n\n\n

Ex 2A Solutions<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
(i) x5<\/sup>-2x3<\/sup>+x+7 is a polynomial and its degree is 5
(ii) y3<\/sup>-\u221a3y is a polynomial and its degree is 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
(i) Degree is 1
(ii) degree is 3
(iii) degree is zero
(iv) degree is 7
(v) degree is 10
(vi) degree is 2<\/p>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
(i) Coefficient of x3<\/sup> is -5.
(ii) Coefficient of x is -2\u221a2
(iii) Coefficient of x2<\/sup> is \u03c03
(iv) Coefficient of x2<\/sup> is 0<\/p>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
(i) Example of a binomial of degree 27 is 4x27<\/sup> \u2013 5
(ii) Example of a monomial of degree 16 is x16<\/sup>
(iii) Example of trinomial of degree 3 is 2x3<\/sup> + 7x + 4<\/p>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
(i) 2x2<\/sup> + 4x is a quadratic polynomial. (Degree 2)
(ii) x \u2013 x3<\/sup> is a cubic polynomial (Degree 3)
(iii) 2 \u2013 y \u2013 y2<\/sup> is a quadratic polynomial (Degree 2)
(iv) \u2013 7 + z is a linear polynomial (Degree 1)
(v) 5t is a linear polynomial (Degree 1)
(vi) p3<\/sup> is a cubic polynomial (Degree 3)<\/p>\n\n\n\n

Ex 2B Solutions<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
p(x) = 5 \u2013 4x + 2x2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
p(y) = 4 + 3y \u2013 y2<\/sup> + 5y3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
f(t)=4t2<\/sup>-3t+6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Ex 2C<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
f(x) = (x3<\/sup> \u2013 6x2<\/sup> + 9x + 3)
Let x-1 = 0, then x = 1
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
f(x) = 2x3<\/sup> \u2013 5x2<\/sup> + 9x \u2013 8)
Let x-3 = 0, then x = 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
f(x) = (3x4<\/sup> \u2013 6x2<\/sup> \u2013 8x + 2)
Let x-2 = 0, the x = 2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
f(x) = (x3<\/sup> \u2013 7x2<\/sup> + 6x + 4)
Let x-6 = 0,then x=6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
f(x)=(x3<\/sup> \u2013 6x2<\/sup> + 13x + 60)
Let x+2=0,then x=-2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
f(x)=(2x4<\/sup> + 6x3<\/sup> + 2x2<\/sup> + x \u2013 8)
Let x+3=0,then x=-3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
f(x)=(4x3<\/sup> \u2013 12x2<\/sup> + 11x \u2013 5)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
f(x)=(81x4<\/sup> + 54x3<\/sup> \u2013 9x2<\/sup> \u2013 3x + 2)<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
f(x)=(x3<\/sup> \u2013 ax2<\/sup> + 2x \u2013 a)
let x-a=0, then x=a
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
f(x)=(ax3<\/sup>+ 3x2<\/sup> \u2013 3)
g(x)=(2x3<\/sup> -5x + a)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
f(x)=x4<\/sup> \u2013 2x3<\/sup> + 3x2<\/sup> \u2013 ax + b
let x-1=0, then x=1
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
By factor theorem, x \u2013 2 will be a factor of f(x) = x3<\/sup> \u2013 8 if f(2) = 0
(\u2234 x-2 = 0=>x = 2)
Now f(2) = (2)3<\/sup> \u2013 8 = 8- 8 = 0
Hence (x \u2013 2) is a factor of f(x) Ans.<\/p>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
By factor theorem,
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
By factor theorem,
(x \u2013 1) is a factor of f(x)=(2x4<\/sup> + 9x3<\/sup> + 6x2<\/sup>\u2013 11x \u2013 6)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
By factor theorem, (x + 2) will
a factor of f (x) = x4<\/sup> \u2013 x4<\/sup> + 2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
By factor theorem, (x + 5) will be a factor of f(x) = 2x3<\/sup> + 9x2<\/sup> \u2013 11x \u2013 30 if f(-5) = 0
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
By factor theorem, (2x \u2013 3) is a factor of f(x) = 2x4<\/sup> + x3<\/sup> \u2013 8x2<\/sup> \u2013 x + 6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
By factor theorem, (x \u2013 \u221a2 ) will be a factor of f(x) = 7x2<\/sup> \u2013 4\u221a2x \u2013 6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
By factor theorem, (x + \u221a2) will be a factor of f(x) = 2\u221a2 x3<\/sup> + 5x + \u221a2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
Let f(x) = 2x3<\/sup> + 9x2<\/sup> + x + k and x \u2013 1 is a factor of f(x)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
Let f(x) = 2x3<\/sup> \u2013 3x2<\/sup> \u2013 18x + a and x \u2013 4 is its factor
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
Let f(x) \u2013 x4<\/sup> \u2013 x3<\/sup> \u2013 11x2<\/sup> \u2013 x + a
f(x) is divisible by (x + 3)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
Let f(x) = 2x3<\/sup> + ax2<\/sup> + 11x + a + 3
and (2x \u2013 1) is its factor
Let 2x \u2013 1 = 0 then 2x = 1
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
Let f(x) = x3<\/sup> \u2013 10x2<\/sup> + ax + b and (x \u2013 1) and (x \u2013 2) are its factors
\u2234 x \u2013 1 = 0 =>x=1
and x \u2013 2 = 2 =>x=2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
Let f(x) = x4<\/sup> + ax3<\/sup> \u2013 7x2<\/sup> \u2013 8x + b ,
and (x + 2) and (x + 3) are its factors
\u2234x + 2 = 0 => x = -2
and x + 3= 0 => x = -3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
Let f(x) = x3<\/sup> \u2013 3x2<\/sup> \u2013 13x + 15
Now x2<\/sup> + 2x \u2013 3 = x2<\/sup> + 3x \u2013 x \u2013 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
Let f(x) = x3<\/sup> + ax2<\/sup> + bx + 6 and (x \u2013 2) is its factor
Let x \u2013 2 = 0 then x = 2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Ex 2E<\/h4>\n\n\n\n

Factorize:<\/strong><\/p>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
9x2<\/sup> + 12xy
= 3x (3x + 4y) Ans.<\/p>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
18x2<\/sup>y \u2013 24xyz
= 6xy (3x \u2013 4z) Ans.<\/p>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
27a3<\/sup>b3<\/sup> \u2013 45a4<\/sup>b2<\/sup>
= 9a3<\/sup>b2<\/sup> (3b \u2013 5a) Ans.<\/p>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
2a (x + y) \u2013 3b(x + y)
= (x + y) (2a \u2013 3b) Ans.<\/p>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
2x (p2<\/sup> + q2<\/sup>) + 4y (p2<\/sup> + q2<\/sup>)
= 2(p2<\/sup> + q2<\/sup>) (x + 2y) Ans<\/p>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
x (a \u2013 5) + y (5 \u2013 a)
= x (a \u2013 5) -y (a \u2013 5)
= (a \u2013 5) (x \u2013 y) Ans.<\/p>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
4(a + b) \u2013 6 (a + b)2<\/sup>
= 2(a + b) {2 \u2013 3 (a + b)}
= 2(a + b) (2 \u2013 3a \u2013 3b) Ans.<\/p>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
8(3a \u2013 2b)2<\/sup> \u2013 10 (3a \u2013 2b)
= 2(3a \u2013 2b) {4 (3a \u2013 2b) \u2013 5}
= 2(3a \u2013 2b) (12a \u2013 8b \u2013 5) Ans.<\/p>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
x (x + x)3<\/sup> \u2013 3x2<\/sup> y (x + y)
= x (x + y) {(x + y)2<\/sup> \u2013 3xy}
= x (x + y) [x2<\/sup> + y2<\/sup> + 2xy \u2013 3xy)
= x (x + y) (x2<\/sup> + y2<\/sup> \u2013 xy) Ans.<\/p>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
x3<\/sup> + 2x2<\/sup> + 5x + 10
= x2<\/sup> (x + 2) + 5 (x + 2)
= (x + 2) (x2<\/sup> + 5) Ans.<\/p>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
x2<\/sup> + xy \u2013 2xz \u2013 2yz
= x (x + y) -2z (x + y)
= (x + y) (x \u2013 2z) Ans.<\/p>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
a3<\/sup> b \u2013 a2<\/sup>b + 5ab \u2013 5b.
= b (a3<\/sup> \u2013 a2<\/sup> + 5a \u2013 5)
= b {(a2<\/sup> (a \u2013 1) + 5 (a \u2013 1)}
= b (a \u2013 1) (a2<\/sup> + 5) Ans.<\/p>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
8 \u2013 4a \u2013 2a3<\/sup> + a4<\/sup>
= 4 (2 \u2013 a) \u2013 a3<\/sup> (2 \u2013 a)
= (2 \u2013 a) (4 \u2013 a3<\/sup>) Ans.<\/p>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
x3<\/sup> \u2013 2x2<\/sup>y + 3xy2<\/sup> \u2013 6y3<\/sup>
= x2<\/sup> (x \u2013 2y) + 3y2<\/sup> (x \u2013 2y)
= (x \u2013 2y) (x2<\/sup> + 3y2<\/sup>) Ans<\/p>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
px \u2013 5q + pq \u2013 5x
= px \u2013 5x + pq \u2013 5q
= x(p \u2013 5) + q(p \u2013 5)
= {p \u2013 5) (x + q) Ans.<\/p>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
x2<\/sup> + y \u2013 xy \u2013 x
= x2<\/sup> \u2013 x \u2013 xy + y
= x (x \u2013 1) \u2013 y (x \u2013 1)
= (x \u2013 1) (x \u2013 y) Ans.<\/p>\n\n\n\n

Question 17.<\/strong>
Solution:<\/strong>
(3a \u2013 1)2<\/sup> \u2013 6a + 2
= (3a \u2013 1)2<\/sup> \u2013 2 (3a \u2013 1)
= (3a \u2013 1) (3a \u2013 1 \u2013 2)
= (3a \u2013 1) (3a \u2013 3)
= 3(3a \u2013 1) (a \u2013 1) Ans.<\/p>\n\n\n\n

Question 18.<\/strong>
Solution:<\/strong>
(2x \u2013 3)2<\/sup> \u2013 8x + 12
= (2x \u2013 3)2<\/sup> \u2013 4(2x \u2013 3)
= (2x \u2013 3) (2x \u2013 3 \u2013 4)
= (2x \u2013 3) (2x \u2013 7) Ans.<\/p>\n\n\n\n

Question 19.<\/strong>
Solution:<\/strong>
a3 + a \u2013 3a2 \u2013 3
= a3 \u2013 3a2 + a \u2013 3
= a2 (a \u2013 3) + 1 (a \u2013 3)
= (a \u2013 3) (a2 + 1) Ans.<\/p>\n\n\n\n

Question 20.<\/strong>
Solution:<\/strong>
3ax \u2013 6ay \u2013 8by + 4bx
= 3ax \u2013 6ay + 4bx \u2013 8by
= 3a (x \u2013 2y) + 4b (x \u2013 2y)
= (x \u2013 2y) (3a + 4b) Ans<\/p>\n\n\n\n

Question 21.<\/strong>
Solution:<\/strong>
abx2<\/sup> + a2<\/sup>x + b2<\/sup>x + ab
= ax (bx + a) + b (bx + a)
= (bx + a) (ax + b) Ans.<\/p>\n\n\n\n

Question 22.<\/strong>
Solution:<\/strong>
x3<\/sup> \u2013 x2<\/sup> + ax + x \u2013 a \u2013 1
= x3<\/sup> \u2013 x2<\/sup> + ax \u2013 a + x \u2013 1
= x2<\/sup> (x \u2013 1) + a (x \u2013 1) + 1 (x \u2013 1)
= (x \u2013 1) (x2<\/sup> + a + 1) Ans.<\/p>\n\n\n\n

Question 23.<\/strong>
Solution:<\/strong>
2x + 4y \u2013 8xy \u2013 1
= 2x \u2013 8xy -1+4y
= 2x (1 \u2013 4y) -1 (1 \u2013 4y)
= (1 \u2013 4y) (2x \u2013 1) Ans.<\/p>\n\n\n\n

Question 24.<\/strong>
Solution:<\/strong>
ab (x2<\/sup> +y2<\/sup>) \u2013 xy (a2<\/sup> + b2<\/sup>)
= abx2<\/sup> + aby2<\/sup> \u2013 a2<\/sup>xy \u2013 b2<\/sup>xy
= abx2<\/sup> \u2013 a2<\/sup>xy \u2013 b2<\/sup>xy + aby2<\/sup>
= ax (bx \u2013 ay) \u2013 by (bx \u2013 ay)
= (bx \u2013 ay) (ax \u2013 by) Ans.<\/p>\n\n\n\n

Question 25.<\/strong>
Solution:<\/strong>
a2<\/sup> + ab (b + 1) + b3<\/sup>
= a2<\/sup> + ab2<\/sup> + ab + b3<\/sup>
= a (a + b2<\/sup>) + b (a + b2<\/sup>)
= (a + b2<\/sup>) (a + b) Ans<\/p>\n\n\n\n

Question 26.<\/strong>
Solution:<\/strong>
a3<\/sup> + ab (1 \u2013 2a) \u2013 2b2<\/sup>
= a3<\/sup> + ab \u2013 2a2<\/sup>b \u2013 2b2<\/sup>
= a3<\/sup> \u2013 2a2<\/sup>b + ab \u2013 2b2<\/sup>
= a2<\/sup> (a \u2013 2b) + b (a \u2013 2b)
= (a \u2013 2b) (a2<\/sup> + b) Ans.<\/p>\n\n\n\n

Question 27.<\/strong>
Solution:<\/strong>
2a2<\/sup> + bc \u2013 2ab \u2013 ac
= 2a2<\/sup> \u2013 2ab \u2013 ac + bc
= 2a (a \u2013 b) \u2013 c (a \u2013 b)
= (a \u2013 b) (2a \u2013 c) Ans.<\/p>\n\n\n\n

Question 28.<\/strong>
Solution:<\/strong>
(ax + by)2<\/sup> + (bx \u2013 ay)2<\/sup>
= a2<\/sup>x2<\/sup> + b2<\/sup>y2<\/sup> + 2abxy + b2<\/sup>x2<\/sup> + a2<\/sup>y2<\/sup> \u2013 2bxy
= a2<\/sup>x2<\/sup> + b2<\/sup>y2<\/sup> + b2<\/sup>x2<\/sup> + a2<\/sup>y2<\/sup>
= a2<\/sup>x2<\/sup> + b2<\/sup>x2<\/sup> + a2<\/sup>y2<\/sup> + b2<\/sup>y2<\/sup>
= x2(a2 + b2) + y2(a2 + b2)
= (a2<\/sup> + b2<\/sup>) (x2<\/sup> + y2<\/sup>) Ans.<\/p>\n\n\n\n

Question 29.<\/strong>
Solution:<\/strong>
a (a + b \u2013 c) \u2013 bc
= a2<\/sup> + ab \u2013 ac \u2013 bc
= a (a + b) \u2013 c (a + b)
(a + b) (a \u2013 c) Ans.<\/p>\n\n\n\n

Question 30.<\/strong>
Solution:<\/strong>
a(a \u2013 2b \u2013 c) + 2bc
= a2<\/sup> \u2013 2ab \u2013 ac +2bc
= a2<\/sup> \u2013 ac \u2013 2ab + 2bc
= a (a \u2013 c) \u2013 2b (a \u2013 c)
= (a \u2013 c) (a \u2013 2b) Ans.<\/p>\n\n\n\n

Question 31.<\/strong>
Solution:<\/strong>
a2<\/sup>x2<\/sup> + (ax2<\/sup> + 1) x + a
= a2<\/sup>x2<\/sup> + ax3<\/sup> + x + a
= a2<\/sup>x2<\/sup> + ax3<\/sup> + a + x
= ax2<\/sup> (a + x) + 1 (a + x)
\u2013 (a + x) (ax2<\/sup> + 1) Ans<\/p>\n\n\n\n

Question 32.<\/strong>
Solution:<\/strong>
ab (x2<\/sup> + 1) + x (a2<\/sup> + b2<\/sup>)
= abx2<\/sup> + ab + a2<\/sup>x + b2<\/sup>x
= abx2<\/sup> + a2<\/sup>x + b2<\/sup>x + ab
= ax (bx + a) + b (bx + a)
= (bx + a) (ax + b) Ans.<\/p>\n\n\n\n

Question 33.<\/strong>
Solution:<\/strong>
x2<\/sup> \u2013 (a + b) x + ab
= x2<\/sup> \u2013 ax \u2013 bx + ab
= x (x \u2013 a) \u2013 b (x \u2013 a)
= (x \u2013 a) (x \u2013 b) Ans.<\/p>\n\n\n\n

Question 34.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Ex 2F<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
25x2<\/sup> \u2013 64y2<\/sup>
= (5x)2<\/sup> \u2013 (8y)2<\/sup>
= (5x + 8y) (5x \u2013 8y) Ans.<\/p>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
100 \u2013 9x2<\/sup>
(10)2<\/sup> \u2013 (3x)2<\/sup>
= (10 + 3x) (10 \u2013 3x) Ans.<\/p>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
5x2<\/sup> \u2013 7y2<\/sup>
=(\u221a5x)2<\/sup> +(\u221a7y)2<\/sup>
=(\u221a5x \u2013 \u221a7y)(\u221a5x \u2013 \u221a7y) Ans<\/p>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
(3x + 5y)2<\/sup> \u2013 4z2<\/sup>
= (3x + 5y)2<\/sup> \u2013 (2z)2<\/sup>
= (3x + 5y + 2z) (3x + 5y \u2013 2z) Ans.<\/p>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
150 \u2013 6x2<\/sup>
= 6(25 \u2013 x2<\/sup>)
= 6{(5)2<\/sup> \u2013 (x2<\/sup>)}
= 6 (5 + x) (5 \u2013 x) Ans.<\/p>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
20x2<\/sup> \u2013 45
= 5 (4x2<\/sup> \u2013 9)
= 5{(2x)2<\/sup> \u2013 (3)2<\/sup>}
= 5 (2x + 3) (2x \u2013 3) Ans.<\/p>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
3x3<\/sup> \u2013 48x
= 3x (x2<\/sup> \u2013 16)
= 3x {(x)2<\/sup> \u2013 (4)2<\/sup>}
= 3x (x + 4) (x \u2013 4) Ans.<\/p>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
2 \u2013 50x2<\/sup>
= 2(1 \u2013 25x2<\/sup>) = 2 {(1)2<\/sup> \u2013 (5x)2<\/sup>}
= 2 (1 + 5x) (1 \u2013 5x) Ans.<\/p>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
27a2<\/sup> \u2013 48b2<\/sup>
= 3(9a2<\/sup> \u2013 16b2<\/sup>)
= 3 {(3a)2<\/sup> \u2013 (4b)2<\/sup>}
= 3(3a + 4b) (3a \u2013 4b) Ans.<\/p>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
x \u2013 64x3<\/sup>
= x (1 \u2013 64x2<\/sup>)
= x{(1)2<\/sup> \u2013 (8x)2<\/sup>}
= x (1 + 8x) (1 \u2013 8x) Ans.<\/p>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
8ab2<\/sup> \u2013 18a3<\/sup>
= 2a (4b2<\/sup> \u2013 9a2<\/sup>)
= 2a {(2b)2<\/sup> \u2013 (3a)2<\/sup>}
= 2a (2b + 3a) (2b \u2013 3a) Ans<\/p>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
3a3<\/sup>b \u2013 243ab3<\/sup>
= 2ab (a2<\/sup> -81 b2<\/sup>)
= 3ab {(a)2<\/sup> \u2013 (9b)2<\/sup>}
= 3ab (a + 9b) (a \u2013 9b) Ans.<\/p>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
(a + b)3<\/sup> \u2013 a \u2013 b
= (a + b)3<\/sup> \u2013 1 (a + b)
= (a + b) {(a + b)2<\/sup> \u2013 1}
= (a + b) {(a + b)2<\/sup> \u2013 (1)2<\/sup>}
= (a + b) (a + b + 1) (a + b \u2013 1) Ans.<\/p>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
108 a2<\/sup> \u2013 3(b \u2013 c)2<\/sup>
= 3 {36a2<\/sup> \u2013 (b \u2013 c)2<\/sup>}
= 3 {(6a)2<\/sup> \u2013 (b \u2013 c)2<\/sup>}
= 3 {(6a + (b \u2013 c)} {6a \u2013 (b \u2013 c)}
= 3 (6a + b \u2013 c) (6a \u2013 b + c) Ans.<\/p>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
x3<\/sup> \u2013 5x2<\/sup> \u2013 x + 5
= x2<\/sup>(x \u2013 5) -1(x \u2013 5)
= (x \u2013 5) (x2<\/sup> \u2013 1)
= (x \u2013 5) {(x)2<\/sup> \u2013 (1)2<\/sup>}
= (x \u2013 5) (x + 1) (x \u2013 1) Ans.<\/p>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
a2<\/sup> + 2ab + b2<\/sup> \u2013 9c2<\/sup>
= (a + b)2<\/sup> \u2013 (3c)2<\/sup>
= {a2<\/sup> + b2<\/sup> + 2ab \u2013 (a + b)2<\/sup>}
= (a + b + 3c) (a + b \u2013 3c) Ans.<\/p>\n\n\n\n

Question 17.<\/strong>
Solution:<\/strong>
9 \u2013 a2<\/sup> + 2ab \u2013 b2<\/sup>
= 9 \u2013 (a2<\/sup> \u2013 2ab + b2<\/sup>)
= (3)2<\/sup> -(a- b)2<\/sup>
{ \u2234a2<\/sup> + b2<\/sup> \u2013 2ab = (a \u2013 b)2<\/sup>}
= (3 + a \u2013 b) (3 \u2013 a + b) Ans.<\/p>\n\n\n\n

Question 18.<\/strong>
Solution:<\/strong>
a2 <\/sup>\u2013 b2<\/sup> \u2013 4ac + 4c2<\/sup>
= a2<\/sup> \u2013 4ac + 4c2<\/sup> \u2013 b2<\/sup>
= (a)2<\/sup> \u2013 2 x a x 2c + (2c)2<\/sup> \u2013 (b)2<\/sup>
= (a \u2013 2c)2<\/sup> \u2013 (b)2<\/sup>
= (a \u2013 2c + b) (a \u2013 2c \u2013 b)
= (a + b \u2013 2c) (a \u2013 b \u2013 2c) Ans.<\/p>\n\n\n\n

Question 19.<\/strong>
Solution:<\/strong>
9a2<\/sup> + 3a \u2013 8B \u2013 64b2<\/sup>
= 9a2<\/sup> \u2013 64b2<\/sup> + 3a \u2013 8b
= (3a)2<\/sup> \u2013 (8b)2<\/sup> + 1(3a \u2013 8b)
= (3a + 8b) (3a \u2013 8b) + 1 (3a \u2013 8b)
= (3a \u2013 8b) (3a + 8b + 1) Ans.<\/p>\n\n\n\n

Question 20.<\/strong>
Solution:<\/strong>
x2<\/sup> \u2013 y2<\/sup> + 6y _ 9
= (x)2 \u2013 (y2<\/sup> \u2013 6y + 9)
= (x)2 \u2013 {(y)2<\/sup> \u2013 2 x y x 3 + (3)2<\/sup>}
= (x)2<\/sup> \u2013 (y \u2013 3)2<\/sup>
= (x + y \u2013 3) (x \u2013 y + 3) Ans.<\/p>\n\n\n\n

Question 21.<\/strong>
Solution:<\/strong>
4x2<\/sup> \u2013 9y2<\/sup> \u2013 2x \u2013 3y
= (2x)2<\/sup> \u2013 (3y)2<\/sup> \u2013 1(2x + 3y)
= (2x + 3y) (2x \u2013 3y) \u2013 1( 2x + 3y)
= (2x + 3y) (2x \u2013 3y \u2013 1) Ans.<\/p>\n\n\n\n

Question 22.<\/strong>
Solution:<\/strong>
x4<\/sup> \u2013 1
= (x2<\/sup>)2<\/sup> \u2013 (1)2<\/sup>
= (x2<\/sup> + 1) (x2<\/sup> \u2013 1)
= (x2<\/sup> + 1) {(x)2<\/sup> \u2013 (1)2<\/sup>}
= (x2<\/sup> + 1) (x + 1) (x \u2013 1) Ans.<\/p>\n\n\n\n

Question 23.<\/strong>
Solution:<\/strong>
a \u2013 b \u2013 a2<\/sup>+ b2<\/sup>
= 1 (a \u2013 b) \u2013 (a2<\/sup> \u2013 b2<\/sup>)
= 1 (a \u2013 b) \u2013 (a + b) (a \u2013 b)
= (a \u2013 b) (1 \u2013 a \u2013 b) Ans.<\/p>\n\n\n\n

Question 24.<\/strong>
Solution:<\/strong>
x4<\/sup> \u2013 625<\/strong>
= (x2<\/sup>)2<\/sup> \u2013 (25)2<\/sup>
= (x2<\/sup> + 25) (x2<\/sup> \u2013 25)
= (x2<\/sup> + 25) {(x)2<\/sup> \u2013 (5)2<\/sup>}
= (x2<\/sup> + 25) (x + 5) (x \u2013 5) Ans.<\/p>\n\n\n\n

Ex 2G<\/p>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
x2<\/sup> + 11x + 30
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
x2<\/sup> + 18x + 32
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
x2<\/sup> + 7x \u2013 18
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
x2<\/sup> + 5x \u2013 6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
y2<\/sup> \u2013 4y + 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
x2<\/sup> \u2013 21x + 108
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
x2<\/sup> \u2013 11x \u2013 80
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
x2<\/sup> \u2013 x \u2013 156
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
z2<\/sup> \u2013 32z \u2013 105
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
40 + 3x \u2013 x2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
6 \u2013 x \u2013 x2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
7x2<\/sup> + 49x + 84
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
m2<\/sup> + 17mn \u2013 84n2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
5x2<\/sup> + 16x + 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
6x2<\/sup> + 17x + 12
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
9x2<\/sup> + 18x + 8
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 17.<\/strong>
Solution:<\/strong>
14x2<\/sup> + 9x + 1
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 18.<\/strong>
Solution:<\/strong>
2x2<\/sup> + 3x \u2013 90
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 19.<\/strong>
Solution:<\/strong>
2x2<\/sup> + 11x \u2013 21
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 20.<\/strong>
Solution:<\/strong>
3x2<\/sup> \u2013 14x + 8
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 21.<\/strong>
Solution:<\/strong>
18x2<\/sup> + 3x- 10
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 22.<\/strong>
Solution:<\/strong>
15x2<\/sup> + 2x \u2013 8
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 23.<\/strong>
Solution:<\/strong>
6x2<\/sup> + 11x \u2013 10
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 24.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 25.<\/strong>
Solution:<\/strong>
24x2<\/sup> \u2013 41x + 12
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 26.<\/strong>
Solution:<\/strong>
2x2<\/sup> \u2013 7x \u2013 15
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 27.<\/strong>
Solution:<\/strong>
6x2<\/sup> \u2013 5x \u2013 21
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 28.<\/strong>
Solution:<\/strong>
10x2<\/sup> \u2013 9x \u2013 7
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 29.<\/strong>
Solution:<\/strong>
5x2<\/sup> \u2013 16x \u2013 21
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 30.<\/strong>
Solution:<\/strong>
2x2<\/sup> \u2013 x \u2013 21
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 31.<\/strong>
Solution:<\/strong>
15x2<\/sup> \u2013 x \u2013 28
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 32.<\/strong>
Solution:<\/strong>
8a2<\/sup> \u2013 27ab + 9b2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 33.<\/strong>
Solution:<\/strong>
5x2<\/sup> + 33xy -14y2<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 34.<\/strong>
Solution:<\/strong>
3x3<\/sup> \u2013 x2<\/sup> \u2013 10x
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 35.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 36.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 37.<\/strong>
Solution:<\/strong>
\u221a2x2<\/sup> + 3x + \u221a2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 38.<\/strong>
Solution:<\/strong>
\u221a5x2<\/sup> + 2x \u2013 3\u221a5
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 39.<\/strong>
Solution:<\/strong>
2a2<\/sup> + 3\u221a3x + 3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 40.<\/strong>
Solution:<\/strong>
2\u221a3x\u00b2 + x \u2013 5\u221a3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 41.<\/strong>
Solution:<\/strong>
5\u221a5x2<\/sup> + 20x + 3\u221a5<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 42.<\/strong>
Solution:<\/strong>
7\u221ax\u00b2 \u2013 10x \u2013 4\u221a2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 43.<\/strong>
Solution:<\/strong>
6\u221a3 x2<\/sup> \u2013 47x + 5\u221a3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 44.<\/strong>
Solution:<\/strong>
7x2<\/sup> + 2\u221a14x + 2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 45.<\/strong>
Solution:<\/strong>
2(x + y)2<\/sup> \u2013 9(x + y) \u2013 5
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 46.<\/strong>
Solution:<\/strong>
9(2a-b)2<\/sup>-4(2a-b)-13
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 47.<\/strong>
Solution:<\/strong>
7(x \u2013 2y)2<\/sup> \u2013 25 (x \u2013 2y) + 12
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 48.<\/strong>
Solution:<\/strong>
4x4<\/sup> + 7x2<\/sup>-2
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Ex 2H<\/h4>\n\n\n\n

Question 1.
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
9x2<\/sup> + 16y2<\/sup> + 4z2<\/sup> \u2013 24xy + 16yz \u2013 12xz
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
25x2<\/sup> + 4y2<\/sup> + 9z2<\/sup> \u2013 20xy \u2013 12yz + 30xz
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Ex 2I<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
(i)(3x+2)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
(i)(95)3<\/sup> = (100 \u2013 5)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Ex 2J<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
x3<\/sup> + 27
= (x)3<\/sup> + (3)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
8x3<\/sup> + 27y3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
343 + 125b3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
(1)3<\/sup>+(4x)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
125a3<\/sup>+ 18
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
216x3<\/sup>+1125
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
16x4<\/sup> + 54x
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
7a3<\/sup> + 56b3<\/sup>
=7(a3<\/sup>+8b3<\/sup>)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
x5<\/sup> + x2<\/sup>
=x2<\/sup>(x3<\/sup>+1)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
a3<\/sup> + 0.008
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
x6<\/sup> + y6<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
2a3<\/sup> + 16b3<\/sup> \u2013 5a \u2013 10b
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
x3<\/sup> \u2013 512
=(x)3 <\/sup>\u2013 (8)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
64x3<\/sup> \u2013 343
=(4x)3 <\/sup>\u2013 (7)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
1 \u2013 27x3<\/sup>
=(1)3<\/sup>\u2013 (3x)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
x3<\/sup> \u2013 125y3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 17.<\/strong>
Solution:<\/strong>
8x3<\/sup> \u2013 127y3
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 18.<\/strong>
Solution:<\/strong>
a3<\/sup> \u2013 0.064
=(a)3 <\/sup>\u2013 (0.4)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 19.<\/strong>
Solution:<\/strong>
(a + 6)3<\/sup> \u2013 8
=(a+b)3 <\/sup>\u2013 (2)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 20.<\/strong>
Solution:<\/strong>
x6<\/sup> \u2013 729
=(x2<\/sup>)3 <\/sup>\u2013 (9)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 21.<\/strong>
Solution:<\/strong>
(a + b)3<\/sup> \u2013 (a \u2013 b)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 22.<\/strong>
Solution:<\/strong>
x \u2013 8xy3<\/sup>
=x(1 \u2013 8y3<\/sup>)
=x{(1)3 <\/sup>\u2013 (2y)3<\/sup>}
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 23.<\/strong>
Solution:<\/strong>
32x4<\/sup> \u2013 500x
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 24.<\/strong>
Solution:<\/strong>
3a7<\/sup>b \u2013 81a4<\/sup> b4<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 25.<\/strong>
Solution:<\/strong>
a3\u22121a3\u22122a+2a
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 26.<\/strong>
Solution:<\/strong>
8a3<\/sup> \u2013 b3<\/sup> \u2013 4ax + 2bx
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 27.<\/strong>
Solution:<\/strong>
a3<\/sup> + 3a2<\/sup>b + 3ab2<\/sup> + b3<\/sup> \u2013 8
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Ex 2K<\/h4>\n\n\n\n

Question 1.<\/strong>
Solution:<\/strong>
125a3<\/sup> + b3<\/sup> + 64c3<\/sup> \u2013 60abc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 2.<\/strong>
Solution:<\/strong>
a3<\/sup> + 8b3<\/sup> + 64c3<\/sup> \u2013 24abc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 3.<\/strong>
Solution:<\/strong>
1 + b3<\/sup> + 8c3<\/sup> \u2013 6bc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 4.<\/strong>
Solution:<\/strong>
216 + 27b3<\/sup> + 8c3<\/sup> \u2013 108bc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 5.<\/strong>
Solution:<\/strong>
27a3<\/sup> \u2013 b3<\/sup> + 8c3<\/sup> + 18abc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 6.<\/strong>
Solution:<\/strong>
8a3<\/sup> + 125b3<\/sup> \u2013 64c3<\/sup> + 120abc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 7.<\/strong>
Solution:<\/strong>
8 \u2013 27b3<\/sup> \u2013 343c3<\/sup> \u2013 126bc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 8.<\/strong>
Solution:<\/strong>
125 \u2013 8x3<\/sup> \u2013 27y3<\/sup> \u2013 90xy
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 9.<\/strong>
Solution:<\/strong>
2\u221a2a3<\/sup> + 16\u221a2b3<\/sup> + c3<\/sup> \u2013 12abc
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 10.<\/strong>
Solution:<\/strong>
x3<\/sup> + y3<\/sup> \u2013 12xy + 64
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 11.<\/strong>
Solution:<\/strong>
(a \u2013 b)3<\/sup> + (b \u2013 c)3<\/sup> + (c \u2013 a)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 12.<\/strong>
Solution:<\/strong>
(3a \u2013 2b)3<\/sup> + (26 \u2013 5c)3<\/sup> + (5c \u2013 3a)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 13.<\/strong>
Solution:<\/strong>
a3<\/sup> (b \u2013 c)3<\/sup> + b3<\/sup> (c \u2013 a)3<\/sup> + c3<\/sup> (a \u2013 b)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 14.<\/strong>
Solution:<\/strong>
(5a \u2013 7b)3<\/sup> + (9c \u2013 5a)3<\/sup> + (7b \u2013 9c)3<\/sup>
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 15.<\/strong>
Solution:<\/strong>
(x + y \u2013 z) (x2<\/sup> + y2<\/sup> + z2<\/sup> \u2013 xy + yz + zx)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 16.<\/strong>
Solution:<\/strong>
(x \u2013 2y + 3) (x2<\/sup> + 4y2<\/sup> + 2xy -3x + 6y + 9)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 17.<\/strong>
Solution:<\/strong>
(x \u2013 2y \u2013 z) (x2<\/sup> + 4y2<\/sup> + z2<\/sup> + 2xy + zx- 2yz)
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 18.<\/strong>
Solution:<\/strong>
x + y + 4 = 0,
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Question 19.<\/strong>
Solution:<\/strong>
x = 2y + 6
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

RS Aggarwal Solutions for Class 9 Maths Chapter 2: Download PDF<\/strong><\/h2>\n\n\n\n

RS Aggarwal Solutions for Class 9 Maths Chapter 2\u2013Polynomials<\/p>\n\n\n\n

Download PDF<\/strong>: RS Aggarwal Solutions for Class 9 Maths Chapter 2\u2013Polynomials PDF<\/a><\/p>\n\n\n\n

Chapterwise RS Aggarwal Solutions for Class 9 Maths :<\/strong><\/h2>\n\n\n\n