Selina Class 8 ICSE Solutions Mathematics : Chapter 12- Algebraic Identities

Class 8: Maths Chapter 12 solutions. Complete Class 8 Maths Chapter 12 Notes.

Selina Class 8 ICSE Solutions Mathematics : Chapter 12- Algebraic Identities

Selina 8th Maths Chapter 12, Class 8 Maths Chapter 12 solutions

Exercise 12A

Question 1.
Use direct method to evaluate the following products :
(i) (x + 8)(x + 3)
(ii) (y + 5)(y – 3)
(iii) (a – 8)(a + 2)
(iv) (b – 3)(b – 5)
(v) (3x – 2y)(2x + y)
(vi) (5a + 16)(3a – 7)
(vii) (8 – b) (3 + b)
Solution:

Question 2.
Use direct method to evaluate :

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Use the product (a + b) (a – b) = a² – b² to evaluate:
(i) 21 × 19
(ii) 33 × 27
(iii) 103 × 97
(iv) 9.8 × 10.2
(v) 7.7 × 8.3
(vi) 4.6 × 5.4
Solution:

Question 5.
Evaluate :
(i) (6 – xy) (6 + xy)

Solution:

Exercise 12B

Question 1.
Expand :
(i) (2a + b)²
(ii) (a – 2b)²

Solution:

Question 2.
Find the square of :

Solution:

Question 3.
Evaluate:
Using expansion of (a + b)² or (a – b)²
(i) (208)²
(ii) (92)²
(iii)(415)²
(iv) (188)²
(v) (9.4)²
(vi) (20.7)²
Solution:

Question 4.
Expand :

Solution:

Question 5.
Find the cube of :

Solution:

Exercise 12C

Question 1.
If a  +b = 5 and ab = 6; find a² + b²
Solution:

Question 2.
If a – b = 6 and ab = 16; find a² + b²
Solution:

Question 3.
If a² + b² = 29 and ab = 10 ; find :
(i) a + b
(ii) a – b
Solution:

Question 4.
If a² + b² = 10 and ab = 3; find :
(i) a – b
(ii) a + b
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
If a + b + c = 10 and a² + b² + c² = 38; find ab + bc + ca
Solution:

Question 10.
Find a² + b² + c² ; if a + b + c = 9 and ab + bc + ca = 24
Solution:

Question 11.
Find a + b + c; if a² + b² + c² = 83 and ab + bc + ca = 71
Solution:

Question 12.
If a + b = 6 and ab=8; find a³ + b³
Solution:

Question 13.
If a – b = 3 and ab = 10; find a³ – b³
Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
Solution:

Exercise 12D

Question 1.
Evaluate:

Solution:

Question 2.
Evaluate:

Solution:

Question 3.
Find the square of :

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.
If a² + b² = 41 and ab = 4, find :
(i) a – b
(ii) a + b
Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
Expand :
(i) (3x – 4y + 5z)²
(ii) (2a – 5b – 4c)²
(iii) (5x + 3y)³
(iv) (6a – 7b)³
Solution:

Question 10.
If a + b + c = 9 and ab + bc + ca = 15, find: a² + b² + c².
Solution:

Question 11.
If a + b + c = 11 and a² + b² + c² = 81, find ab + bc + ca.
Solution:

Question 12.
If 3x – 4y = 5 and xy = 3, find : 27x³ – 64y³.
Solution:

Question 13.
If a + b = 8 and ab = 15, find : a³ + b³.
Solution:

Question 14.
If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³
Solution:

Question 15.
If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³
Solution:

Question 16.
The difference between two numbers is 5 and their products is 14. Find the difference between their cubes.
Solution:

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Selina Class 8 ICSE Solutions Mathematics : Chapter 12- Algebraic Identities

Download PDF: Selina Class 8 ICSE Solutions Mathematics : Chapter 12- Algebraic Identities PDF

Chapterwise Selina Publishers ICSE Solutions for Class 8 Mathematics :

• Chapter 1- Rational Numbers
• Chapter 2- Exponents (Powers)
• Chapter 3- Squares and Square Roots
• Chapter 4- Cubes and Cube-Roots
• Chapter 5- Playing with Number
• Chapter 6- Sets
• Chapter 7- Percent and Percentage
• Chapter 8- Profit, Loss and Discount
• Chapter 9- Simple and Compound Interest
• Chapter 10- Direct and Inverse Variations
• Chapter 11- Algebraic Expressions
• Chapter 12- Algebraic Identities
• Chapter 13- Factorisation
• Chapter 14- Linear Equations in one Variable
• Chapter 15- Linear Inequations
• Chapter 16- Understanding Shapes
• Chapter 17- Special Types of Quadrilaterals
• Chapter 18- Constructions
• Chapter 19- Representing 3-D in 2-D
• Chapter 20- Area of Trapezium and a Polygon
• Chapter 21- Surface Area, Volume and Capacity
• Chapter 22- Data Handling
• Chapter 23- Probability

About Selina Publishers ICSE

Selina Publishers has been serving the students since 1976 and is one of the quality ICSE school textbooks publication houses. Mathematics and Science books for classes 6-10 form the core of our business, apart from certain English and Hindi literature as well as a few primary books. All these books are based upon the syllabus published by the Council for the I.C.S.E. Examinations, New Delhi. The textbooks are composed by a panel of subject experts and vetted by teachers practising in ICSE schools all over the country. Continuous efforts are made in complying with the standards and ensuring lucidity and clarity in content, which makes them stand tall in the industry.