{"id":625597,"date":"2023-09-07T08:57:32","date_gmt":"2023-09-07T08:57:32","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=625597"},"modified":"2023-09-07T09:00:53","modified_gmt":"2023-09-07T09:00:53","slug":"kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/","title":{"rendered":"KC Sinha: Exercise 4.2 – Mathematics Solution Class 9 Chapter 4 \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u090f\u0901"},"content":{"rendered":"\n\n\n\n\n

Question 1<\/h4>\n\n\n\n

(i) x2<\/sup>+4x+4<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>=(a+b)(a+b)
\u21d2x2<\/sup>+22<\/sup>+2(x)(2)
\u21d2(x+2)2<\/sup>
\u21d2(x+2)(x+2)
(ii) x2<\/sup>-18x+81<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>-2ab=(a-b)2<\/sup>=(a-b)(a-b)
\u21d2x2<\/sup>+92<\/sup>-2(x)(9)
\u21d2(x-9)2<\/sup>
\u21d2(x-9)(x-9)
(iii) 4x2<\/sup>+4x+1<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>=(a+b)(a+b)
\u21d2(2x)2<\/sup>+12<\/sup>+2(2x)(1)
\u21d2(2x+1)2<\/sup>
\u21d2(2x+1)(2x+1)
(iv) $\\dfrac{4}{9}a^2+b^2+\\dfrac{4}{3}ab$<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>=(a+b)(a+b)
\u21d2$\\left(\\dfrac{2}{3}a\\right)^2+b^2+2\\left(\\dfrac{2}{3}a\\right)(b)$
\u21d2$\\left(\\dfrac{2}{3}a+b\\right)^2$
\u21d2$\\left(\\dfrac{2}{3}a+b\\right)$ $\\left(\\dfrac{2}{3}a+b\\right)$
(v) 25a2<\/sup>-60ab+36b2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>-2ab=(a-b)2<\/sup>=(a-b)(a-b)
\u21d2(5a)2<\/sup>+(6b)2<\/sup>-2(5a)(6b)
\u21d2(5a-6b)2<\/sup>
\u21d2(5a-6b)(5a-6b)
(vi) 9a2<\/sup>-30ab+25b2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>-2ab=(a-b)2<\/sup>=(a-b)(a-b)
\u21d2(3a)2<\/sup>+(5b)2<\/sup>-2(3a)(5b)
\u21d2(3a-5b)2<\/sup>
\u21d2(3a-5b)(3a-5b)
(vii) 4(x-y)2<\/sup>-12(x-y)(x+y)+9(x+y)2<\/sup><\/strong>
Sol:
Using identity:
(a2<\/sup>-b2<\/sup>)=(a+b)(a-b)
\u21d24(x2<\/sup>+y2<\/sup>-2xy)-12(x2<\/sup>-y2<\/sup>)+9(x2<\/sup>+y2<\/sup>+2xy)
\u21d24x2<\/sup>+4y2<\/sup>-8xy-12x2<\/sup>+12y2<\/sup>+9x2<\/sup>+9y2<\/sup>+18xy
\u21d24x2<\/sup>-12x2<\/sup>+9x2<\/sup>+4y2<\/sup>+12y2<\/sup>+9y2<\/sup>-8xy+18xy
\u21d213x2<\/sup>-12x2<\/sup>+13y2<\/sup>+12y2<\/sup>+10xy
\u21d2x2<\/sup>+25y2<\/sup>+10xy
\u21d2x2<\/sup>+(5y)2<\/sup>+2(x)(5y)
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>
\u21d2(x+5y)2<\/sup>
\u21d2(x+5y)(x+5y)<\/p>\n\n\n\n

Question 2<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0928\u093f\u0915\u093e\u0932\u0947
(i) p2<\/sup>+q2<\/sup>+9r2<\/sup>+2pq+6pr+6qr<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca=(a+b+c)2<\/sup>
\u21d2p2<\/sup>+q2<\/sup>+(3r)2<\/sup>+2pq+2(q)(3r)+2(3r)(p)
\u21d2(p+q+3r)2<\/sup>
\u21d2(p+q+3r)(p+q+3r)
(ii) 4a2<\/sup>+9b2<\/sup>+c2<\/sup>+12ab+4ac+6bc<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca=(a+b+c)2<\/sup>
\u21d2(2a)2<\/sup>+(3b)2<\/sup>+c2<\/sup>+2(2a)(3b)+2(3b)(c)+2(c)(2a)
\u21d2(2a+3b+c)2<\/sup>
\u21d2(2a+3b+c)(2a+3b+c)
(iii) x2<\/sup>+4+9z2<\/sup>+4x-6rz-12z<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca=(a+b+c)2<\/sup>
\u21d2(x)2<\/sup>+(2)2<\/sup>+(-3z)2<\/sup>+2(x)(2)+2(2)(-3z)+2(-3z)(x)
\u21d2(x+2-3z)2<\/sup>
\u21d2(x+2-3z)(x+2-3z)
(iv) 4x2<\/sup>+9y2<\/sup>+z2<\/sup>-12xy-4xz+6yz<\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca=(a+b+c)2<\/sup>
\u21d2(-2x)2<\/sup>+(3y)2<\/sup>+(z)2<\/sup>+2(-2x)(3y)+2(3y)(z)+2(z)(-2x)
\u21d2(-2x+3y+z)2<\/sup>
[Taking common (-)]
\u21d2(2x-3y-z)(2x-3y-z)<\/p>\n\n\n\n

Question 4<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947 \u0964
(i) x2<\/sup>-1<\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2x2<\/sup>-12<\/sup>
\u21d2(x-1)(x+1)
(ii) x2<\/sup>-4<\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2x2<\/sup>-22<\/sup>
\u21d2(x-2)(x+2)
(iii) 49-64x2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2(7)2<\/sup>-(8x)2<\/sup>
\u21d2(7-8x)(7+8x)
(iv) 4x2<\/sup>-81<\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2(2x)2<\/sup>-(9)2<\/sup>
\u21d2(2x-9)(2x+9)
(v) 4a2<\/sup>-(2b-c)2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2(2a)2<\/sup>-(2b-c)2<\/sup>
\u21d2[2a+2b-c][2a-(2b-c)]
\u21d2(2a+2b-c)(2a-2b+c)
(vi) 16(2x-1)2<\/sup>-25z2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[4(2x-1)]2<\/sup>-(5z)2<\/sup>
\u21d2[4(2x-1)+5z][4(2x-1)-5z]
\u21d2[8x-4+5z][8x-4-5z]
\u21d2(8a-5z-4)(8x+5z-4)<\/p>\n\n\n\n

(vii)<\/strong> $\\frac{x^2}{4}-\\frac{y^2}{4}$
Sol :<\/p>\n\n\n\n

(viii)<\/strong> 25(x-y)2<\/sup>-4(x+4)2<\/sup>
Sol :<\/p>\n\n\n\n

Question 5<\/h4>\n\n\n\n

\u0928\u093f\u092e\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947 \u0964
(i) x2<\/sup>+y2<\/sup>+2xy-z2<\/sup><\/strong>
Sol:
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>
\u21d2(x+y)2<\/sup>-(z)2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2(x+y+z)(x+y-z)
(ii) x2<\/sup>+y2<\/sup>-z2<\/sup>-2xy<\/strong>
Sol:
Using identity:
a2<\/sup>+b2-<\/sup>2ab=(a-b)2<\/sup>
\u21d2x2<\/sup>+y2<\/sup>-2xy-z2<\/sup>
\u21d2(x-y)2<\/sup>-(z)2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[(x-y)+(z)][(x-y)-(z)]
\u21d2(x-y+z)(x-y-z)
(iii) a2<\/sup>-b2<\/sup>-c2<\/sup>-2bc<\/strong>
Sol:
\u21d2(a)2<\/sup>-(b2<\/sup>+c2<\/sup>+2bc)
Using identity:
x2<\/sup>+y2<\/sup>+2xy=(x+y)2<\/sup>
\u21d2(a)2<\/sup>-(b+c)2<\/sup>
Using identity:
x2<\/sup>-y2<\/sup>=(x+y)(x-y)
\u21d2[(a)+(b+c)][(a)-(b+c)]
\u21d2(a+b+c)(a-b-c)
(iv) x2<\/sup>-1-2a-a2<\/sup><\/strong>
Sol:
\u21d2x2<\/sup>-[a2<\/sup>+12<\/sup>+2(a)(1)]
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>
\u21d2(x)2<\/sup>-(a+1)2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[x+a+1][x-(a+1)]
\u21d2(x+a+1)(x-a-1)
(v) x4<\/sup>-14x2<\/sup>y2<\/sup>+y4<\/sup><\/strong>
Sol:
\u21d2x4<\/sup>+y4<\/sup>-14x2<\/sup>y2<\/sup>
\u21d2[(x2<\/sup>)2<\/sup>+(y2<\/sup>)2<\/sup>+2(x2<\/sup>)(y2<\/sup>)]-[16(x2<\/sup>)(y2<\/sup>)]
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[(x2<\/sup>+y2<\/sup>)2<\/sup>]-[16(x2<\/sup>)(y2<\/sup>)]
\u21d2(x2<\/sup>+y2<\/sup>)2<\/sup>-(4xy)2<\/sup>
\u21d2(x2<\/sup>+y2<\/sup>-4xy)(x2<\/sup>+y2<\/sup>+4xy)
(vi) x4<\/sup>-7x2<\/sup>y2<\/sup>+y4<\/sup><\/strong>
Sol:
\u21d2x4<\/sup>+y4<\/sup>-7x2<\/sup>y2<\/sup>
\u21d2[(x2<\/sup>)2<\/sup>+(y2<\/sup>)2<\/sup>+2(x2<\/sup>)(y2<\/sup>)]-[9x2<\/sup>y2<\/sup>]
Using identity:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>
\u21d2[(x2<\/sup>+y2<\/sup>)2<\/sup>]-[9x2<\/sup>y2<\/sup>]
\u21d2(x2<\/sup>+y2<\/sup>)2<\/sup>-(3xy)2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[(x2<\/sup>+y2<\/sup>)+(3xy)][(x2<\/sup>+y2<\/sup>)-(3xy)]
\u21d2(x2<\/sup>+y2<\/sup>+3xy)(x2<\/sup>+y2<\/sup>-3xy)<\/p>\n\n\n\n

(vii)<\/strong> 4x4<\/sup>+3x2<\/sup>+9
Sol :
=(2x2<\/sup>)2<\/sup>+2.2x2<\/sup>+32<\/sup>-9x2<\/sup>
=(2x2<\/sup>+3)2<\/sup>-(3x)2<\/sup>
=(2x2<\/sup>+3+3x)(2x2<\/sup>+3-3x)<\/p>\n\n\n\n

Question 6<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947 \u0964
(i) (1-x2<\/sup>)(1-y2<\/sup>)+4xy<\/strong>
Sol:
\u21d2(1-x2<\/sup>)\u00d7(1-y2<\/sup>)+4xy
\u21d21\u00d7(1-y2<\/sup>)-x2<\/sup>(1-y2<\/sup>)+4xy
\u21d21-y2<\/sup>-x2<\/sup>+x2<\/sup>y2<\/sup>+4xy
\u21d2(1+2xy+x2<\/sup>y2<\/sup>)-(x2<\/sup>+y2<\/sup>-2xy)
Using identities:
a2<\/sup>+b2<\/sup>+2ab=(a+b)2<\/sup>
a2<\/sup>+b2<\/sup>-2ab=(a-b)2<\/sup>
\u21d2(1+xy)2<\/sup>-(x-y)2<\/sup>
\u21d2[(1+xy)+(x-y)] \u00d7 [( 1+xy)- (x-y)]
\u21d2[(1+x-y+xy) (1-x+y+xy)]<\/p>\n\n\n\n

(ii) c2<\/sup>+2ab-(a2<\/sup>+b2<\/sup>)<\/strong>
Sol:
\u21d2c2<\/sup>+2ab-a2<\/sup>-b2<\/sup>
\u21d2(c)2<\/sup>-(a2<\/sup>+b2<\/sup>-2ab)
Using identity:
a2<\/sup>+b2<\/sup>-2ab=(a-b)2<\/sup>
\u21d2c2<\/sup>-(a-b)2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2(c+a-b)(c-a+b)
(iii) p-2q-p2<\/sup>+4q2<\/sup><\/strong>
Sol:
\u21d2p-2q-p2<\/sup>+4q2<\/sup>
\u21d2p-2q-(p\u00b2-4q\u00b2)
Using identity:
a\u00b2-b\u00b2=(a – b)(a + b)
\u21d2(p-2q)-(p-2q)(p+2q)
[Taking common (p-2q)]
\u21d2(p-2q)(1-p-2q)
(iv) b2<\/sup>+c2<\/sup>+2(ab+bc+ca)<\/strong>
Sol:
adding and subtracting a2<\/sup>
\u21d2a2<\/sup>+b2<\/sup>+c2<\/sup>+2(ab+bc+ca)-a2<\/sup>
\u21d2a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca-a2<\/sup>
Using identity:
x2<\/sup>+y2<\/sup>+z2<\/sup>+2xy+2yz+2zx=(x+y+z)2<\/sup>
\u21d2(a+b+c)2<\/sup>-a2<\/sup>
Using identity:
a2<\/sup>-b2<\/sup>=(a+b)(a-b)
\u21d2[(a+b+c)+a][(a+b+c)-a]
\u21d2(b+c+2a)(b+c)<\/p>\n\n\n\n

Question 7<\/h4>\n\n\n\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947 \u0964<\/p>\n\n\n\n

(i) 27x3<\/sup>+54x2<\/sup>y+36xy2<\/sup>+8y3<\/sup><\/strong>
Sol:
\u21d227x3<\/sup>+8y3<\/sup>+54x2<\/sup>y+36xy2<\/sup>
\u21d2(3x)3<\/sup>+(2y)3<\/sup>+3(3x)2<\/sup>(y)+3(3x)(y)2<\/sup>
Using identity:
a3<\/sup>+b3<\/sup>+3a2<\/sup>b+3ab2<\/sup>=(a+b)3<\/sup>
\u21d2(3x+2y)3<\/sup>
\u21d2(3x+2y)(3x+2y)(3x+2y)
(ii) 8x3<\/sup>+y3<\/sup>+12x2<\/sup>y+6xy2<\/sup><\/strong>
Sol:
\u21d28x3<\/sup>+y3<\/sup>+12x2<\/sup>y+6xy2<\/sup>
\u21d2(2x)3<\/sup>+y3<\/sup>+3(2x)2<\/sup>(y)+3(2x)(y)2<\/sup>
Using identity:
a3<\/sup>+b3<\/sup>+3a2<\/sup>b+3ab2<\/sup>=(a+b)3<\/sup>
\u21d2(2x+y)3<\/sup>
\u21d2(2x+y)(2x+y)(2x+y)<\/p>\n\n\n\n

(iii) a3<\/sup>x3<\/sup>-3a2<\/sup>bx2<\/sup>+3ab2<\/sup>x-b3<\/sup><\/strong>
Sol:
\u21d2a3<\/sup>x3<\/sup>-b3<\/sup>-3a2<\/sup>bx2<\/sup>+3ab2<\/sup>x
\u21d2(ax)3<\/sup>-b3<\/sup>-3(ax)2<\/sup>(b)+3(ax)(b)2<\/sup>
Using identity:
a3<\/sup>-b3<\/sup>-3a2<\/sup>b+3ab2<\/sup>=(a-b)3<\/sup>
\u21d2(ax-b)3<\/sup>
\u21d2(ax-b)(ax-b)(ax-b)
(iv) x3<\/sup>-12x(x-4)-64<\/strong>
Sol:
\u21d2x3<\/sup>-43<\/sup>-12x(x-4)
\u21d2x3<\/sup>-43<\/sup>-12x2<\/sup>+48x
\u21d2x3<\/sup>-43<\/sup>-3(x)2<\/sup>(4)+3(x)(4)2<\/sup>
Using identity:
a3<\/sup>-b3<\/sup>-3a2<\/sup>b+3ab2<\/sup>=(a-b)3<\/sup>
\u21d2(x-4)3<\/sup>
\u21d2(x-4)(x-4)(x-4)
(v) $a^3+\\dfrac{3}{2}a^2+\\dfrac{3}{4}a+\\dfrac{1}{8}$<\/strong>
Sol:
\u21d2$a^3+\\dfrac{1}{8}+\\dfrac{3}{2}a^2+\\dfrac{3}{4}a$
\u21d2$a^3+\\left(\\dfrac{1}{2}\\right)^3+3(a)^2\\left(\\dfrac{1}{2}\\right)+3(a)\\left(\\dfrac{1}{2}\\right)^2$
Using identity:
a3<\/sup>+b3<\/sup>+3a2<\/sup>b+3ab2<\/sup>=(a+b)3<\/sup>
\u21d2$\\left(a+\\dfrac{1}{2}\\right)^3$
\u21d2$\\left(a+\\dfrac{1}{2}\\right)\\left(a+\\dfrac{1}{2}\\right)\\left(a+\\dfrac{1}{2}\\right)$<\/p>\n\n\n\n

(vi)<\/strong> $x^3-x^2y+\\frac{1}{3}xy^2-\\frac{1}{27}y^3$<\/p>\n\n\n\n

Sol :<\/p>\n\n\n\n

=$\\left(x-\\frac{1}{3}y\\right)^3$<\/p>\n\n\n\n

=$\\left(x-\\frac{1}{3}y\\right)\\left(x-\\frac{1}{3}y\\right)\\left(x-\\frac{1}{3}y\\right)$<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 9 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Question 1 (i) x2+4x+4Sol:Using identity:a2+b2+2ab=(a+b)2=(a+b)(a+b)\u21d2x2+22+2(x)(2)\u21d2(x+2)2\u21d2(x+2)(x+2)(ii) x2-18x+81Sol:Using identity:a2+b2-2ab=(a-b)2=(a-b)(a-b)\u21d2x2+92-2(x)(9)\u21d2(x-9)2\u21d2(x-9)(x-9)(iii) 4×2+4x+1Sol:Using identity:a2+b2+2ab=(a+b)2=(a+b)(a+b)\u21d2(2x)2+12+2(2x)(1)\u21d2(2x+1)2\u21d2(2x+1)(2x+1)(iv) $\\dfrac{4}{9}a^2+b^2+\\dfrac{4}{3}ab$Sol:Using identity:a2+b2+2ab=(a+b)2=(a+b)(a+b)\u21d2$\\left(\\dfrac{2}{3}a\\right)^2+b^2+2\\left(\\dfrac{2}{3}a\\right)(b)$\u21d2$\\left(\\dfrac{2}{3}a+b\\right)^2$\u21d2$\\left(\\dfrac{2}{3}a+b\\right)$ $\\left(\\dfrac{2}{3}a+b\\right)$(v) 25a2-60ab+36b2Sol:Using identity:a2+b2-2ab=(a-b)2=(a-b)(a-b)\u21d2(5a)2+(6b)2-2(5a)(6b)\u21d2(5a-6b)2\u21d2(5a-6b)(5a-6b)(vi) 9a2-30ab+25b2Sol:Using identity:a2+b2-2ab=(a-b)2=(a-b)(a-b)\u21d2(3a)2+(5b)2-2(3a)(5b)\u21d2(3a-5b)2\u21d2(3a-5b)(3a-5b)(vii) 4(x-y)2-12(x-y)(x+y)+9(x+y)2Sol:Using identity:(a2-b2)=(a+b)(a-b)\u21d24(x2+y2-2xy)-12(x2-y2)+9(x2+y2+2xy)\u21d24×2+4y2-8xy-12×2+12y2+9×2+9y2+18xy\u21d24×2-12×2+9×2+4y2+12y2+9y2-8xy+18xy\u21d213×2-12×2+13y2+12y2+10xy\u21d2x2+25y2+10xy\u21d2x2+(5y)2+2(x)(5y)Using identity:a2+b2+2ab=(a+b)2\u21d2(x+5y)2\u21d2(x+5y)(x+5y) Question 2 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0928\u093f\u0915\u093e\u0932\u0947(i) p2+q2+9r2+2pq+6pr+6qrSol:Using identity:a2+b2+c2+2ab+2bc+2ca=(a+b+c)2\u21d2p2+q2+(3r)2+2pq+2(q)(3r)+2(3r)(p)\u21d2(p+q+3r)2\u21d2(p+q+3r)(p+q+3r)(ii) 4a2+9b2+c2+12ab+4ac+6bcSol:Using identity:a2+b2+c2+2ab+2bc+2ca=(a+b+c)2\u21d2(2a)2+(3b)2+c2+2(2a)(3b)+2(3b)(c)+2(c)(2a)\u21d2(2a+3b+c)2\u21d2(2a+3b+c)(2a+3b+c)(iii) x2+4+9z2+4x-6rz-12zSol:Using identity:a2+b2+c2+2ab+2bc+2ca=(a+b+c)2\u21d2(x)2+(2)2+(-3z)2+2(x)(2)+2(2)(-3z)+2(-3z)(x)\u21d2(x+2-3z)2\u21d2(x+2-3z)(x+2-3z)(iv) 4×2+9y2+z2-12xy-4xz+6yzSol:Using identity:a2+b2+c2+2ab+2bc+2ca=(a+b+c)2\u21d2(-2x)2+(3y)2+(z)2+2(-2x)(3y)+2(3y)(z)+2(z)(-2x)\u21d2(-2x+3y+z)2[Taking common (-)]\u21d2(2x-3y-z)(2x-3y-z) Question 4 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947 \u0964(i) x2-1Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2x2-12\u21d2(x-1)(x+1)(ii) x2-4Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2x2-22\u21d2(x-2)(x+2)(iii) 49-64x2Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2(7)2-(8x)2\u21d2(7-8x)(7+8x)(iv) 4×2-81Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2(2x)2-(9)2\u21d2(2x-9)(2x+9)(v) 4a2-(2b-c)2Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2(2a)2-(2b-c)2\u21d2[2a+2b-c][2a-(2b-c)]\u21d2(2a+2b-c)(2a-2b+c)(vi) 16(2x-1)2-25z2Sol:Using identity:a2-b2=(a+b)(a-b)\u21d2[4(2x-1)]2-(5z)2\u21d2[4(2x-1)+5z][4(2x-1)-5z]\u21d2[8x-4+5z][8x-4-5z]\u21d2(8a-5z-4)(8x+5z-4) […]<\/p>\n","protected":false},"author":302,"featured_media":625596,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[921],"tags":[],"boards":[],"class_list":["post-625597","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","entry"],"yoast_head":"\nKC Sinha: Exercise 4.2 - Mathematics Solution Class 9 Chapter 4 \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u090f\u0901 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"Question 1 (i) x2+4x+4Sol:Using identity:a2+b2+2ab=(a+b)2=(a+b)(a+b)\u21d2x2+22+2(x)(2)\u21d2(x+2)2\u21d2(x+2)(x+2)(ii) x2-18x+81Sol:Using\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 4.2 - Mathematics Solution Class 9 Chapter 4 \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u090f\u0901\" \/>\n<meta property=\"og:description\" content=\"Question 1 (i) x2+4x+4Sol:Using identity:a2+b2+2ab=(a+b)2=(a+b)(a+b)\u21d2x2+22+2(x)(2)\u21d2(x+2)2\u21d2(x+2)(x+2)(ii) x2-18x+81Sol:Using\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-07T08:57:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-07T09:00:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-1-3-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1600\" \/>\n\t<meta property=\"og:image:height\" content=\"901\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"KC Sinha: Exercise 4.2 – Mathematics Solution Class 9 Chapter 4 \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u090f\u0901\",\"datePublished\":\"2023-09-07T08:57:32+00:00\",\"dateModified\":\"2023-09-07T09:00:53+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\"},\"wordCount\":1187,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2023\/09\/indcareer-schools-2-1-3-scaled.jpg\",\"articleSection\":[\"class 9\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-4-2-mathematics-solution-class-9-chapter-4-bjiy-sarvasamikaye\/\",\"name\":\"KC Sinha: Exercise 4.2 - 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