## Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

**Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities**

### Algebraic Identities Exercise 12A – Selina Concise Mathematics Class 8 ICSE Solutions

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) = a^{2} – b^{2} 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:

### Algebraic Identities Exercise 12B – Selina Concise Mathematics Class 8 ICSE Solutions

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:

### Algebraic Identities Exercise 12C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

If a +b = 5 and ab = 6; find a^{2} + b^{2}

Solution:

Question 2.

If a – b = 6 and ab = 16; find a^{2} + b^{2}

Solution:

Question 3.

If a^{2} + b^{2} = 29 and ab = 10 ; find :

(i) a + b

(ii) a – b

Solution:

Question 4.

If a^{2} + b^{2 }= 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 a^{2} + b^{2} + c^{2} = 38; find ab + bc + ca

Solution:

Question 10.

Find a^{2} + b^{2} + c^{2} ; if a + b + c = 9 and ab + bc + ca = 24

Solution:

Question 11.

Find a + b + c; if a^{2} + b^{2} + c^{2} = 83 and ab + bc + ca = 71

Solution:

Question 12.

If a + b = 6 and ab=8; find a^{3} + b^{3}

Solution:

Question 13.

If a – b = 3 and ab = 10; find a^{3} – b^{3}

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:

### Algebraic Identities Exercise 12D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Evaluate:

Solution:

Question 2.

Evaluate:

Solution:

Question 3.

Find the square of :

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

If a^{2} + b^{2} = 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: a^{2} + b^{2} + c^{2}.

Solution:

Question 11.

If a + b + c = 11 and a^{2} + b^{2} + c^{2} = 81, find ab + bc + ca.

Solution:

Question 12.

If 3x – 4y = 5 and xy = 3, find : 27x^{3} – 64y^{3}.

Solution:

Question 13.

If a + b = 8 and ab = 15, find : a^{3} + b^{3}.

Solution:

Question 14.

If 3x + 2y = 9 and xy = 3, find : 27x^{3} + 8y^{3}

Solution:

Question 15.

If 5x – 4y = 7 and xy = 8, find : 125x^{3} – 64y^{3}

Solution:

Question 16.

The difference between two numbers is 5 and their products is 14. Find the difference between their cubes.

Solution: