## RS Aggarwal Class 8 Solutions Chapter 7 Factorisation Ex 7A

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7A.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7A
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7C
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7D
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7E

**Factorize :**

**Question 1.**

**Solution:**

(i) 12x + 15 = 3(4x + 5) {HCF of 12 and 15 = 3)

(ii) 14m – 21 = 7(2m – 3) {HCF of 14 and 21 = 7)

(iii) 9n – 12n^{2} = 3n(3 – 4n) Ans.{HCF of 9 and 12 = 3}

**Question 2.**

**Solution:**

(i) 16a^{2} – 24ab = 8a(2a – 3b) { HCF of 16 and 24 = 8)

(ii) 15ab^{2} – 20a^{2}b = 5ab(3b – 4a) {HCF of 15 and 20 5}

(iii) 12x^{2}y^{3} – 21x^{3}y^{2}= 3x^{2}y^{2}(4y – 7x) Ans. {HCF of 12 and 21 = 3)

**Question 3.**

**Solution:**

(i) 24x^{3} – 36x^{2}y = 12x^{2}(2x – 3y) {HCF of 24 and 36 = 12}

(ii) 10x^{3} – 15x^{2} = 5x^{2}(2x – 3) {HCF of 10, 15 = 5}

(iii) 36x^{3}y – 60x^{2}y^{3}z = 12x^{2}y (3x – 5y^{2}z) {HCF of 36 and 60 = 12}

**Question 4.**

**Solution:**

(i)9x^{3} – 6x^{2} + 12x

= 3x(3x^{2} – 2x + 4) {HCF of 9, 6, 12 = 3)

(ii)8x^{2} – 72xy + 12x

= 4x(2x – 18y + 3) (HCF of 8, 72, 124)

(iii)18a^{3}b^{3} – 27a^{2}b^{3} + 36a^{3}b^{2}

= 9a^{2}b^{2}(2ab – 3b + 4a) Ans.{HCF of 10, 27, 36 = 9)

**Question 5.**

**Solution:**

(i) 14x^{3} + 21x^{4}y – 28x^{2}y^{2}

= 7x^{2} (2x + 3x^{2}y – 4y^{2}) {HCF of 14, 21 28 = 7)

(ii) – 5 – 10t + 20t^{2}

= – 5(1 + 2t – 4t^{2}) Ans. {HCF of 5, 10, 20=5)

**Question 6.**

**Solution:**

(i) x(x + 3) + 5(x + 3)

=(x + 3)(x + 5)

(ii) 5x(x – 4) – 7(x – 4)

= (x – 4) (5x – 7)

(iii) 2m (1 – n) + 3(1 – n)

= (1 – n) (2m + 3) Ans.

**Question 7.**

**Solution:**

6a(a – 2b) + 5b(a – 2b)

= (a – 2b) (6a + 5b) Ans.

**Question 8.**

**Solution:**

x^{3}(2a – b) + x^{2}(2a – b)

=x^{2}(2a – b)(x + 1)Ans.

**Question 9.**

**Solution:**

9a(3a – 5b) – 12a^{2}(3a – 5b)

= 3a (3a – 5b) (3 – 4a) Ans.

**Question 10.**

**Solution:**

(x + 5)^{2} – 4(x + 5)

= (x + 5)(x + 5 – 4)

=(x + 5)(x + 1)Ans.

**Question 11.**

**Solution:**

3(a – 2b)^{2} – 5 (a – 2b)

= (a – 2b) {3(a – 2b) – 5}

= (a – 2b) (3a – 6b – 5) Ans.

**Question 12.**

**Solution:**

2a + 6b – 3 (a + 3b)^{2}

= 2(a + 3b) – 3(a + 3b)^{2}

= (a + 3b){ 2 – 3 (a + 3b)}

= (a + 3b) (2 – 3a – 9b) Ans.

**Question 13.**

**Solution:**

16(2p – 3q)^{2} – 4 (2p – 3q)

= 4(2p – 3q) {4(2p – 3q) – 1}

= 4(2p – 3q) (8p – 12q – 1) Ans.

**Question 14.**

**Solution:**

x(a – 3) + y (3 – a)

= x(a – 3) – y(a – 3)

= (a – 3) (x – y) Ans.

**Question 15.**

**Solution:**

12(2x – 3y)^{2} – 16(3y – 2x)

= 12(2x – 3y)^{2} + 16(2x – 3y)

= 4(2x – 3y) {3(2x – 3y) + 4}

= 4(2x – 3y) (6x – 9y + 4) Ans.

**Question 16.**

**Solution:**

(x + y)(2x + 5) – (x + y)(x + 3)

= (x + y)(2 + 5 – x – 3)

= (x + y)(x + 2) Ans.

**Question 17.**

**Solution:**

ar + br + at + bt

= r(a + b) + t(a + b)

= (a + b) (r + t) Ans.

**Question 18.**

**Solution:**

x^{2} – ax – bx + ab

= x(x – a) – b(x – a)

= (x – a)(x – b)Ans.

**Question 19.**

**Solution:**

ab^{2} – bc^{2} – ab + c^{2}

= ab^{2} – ab – bc^{2} + c^{2}

= ab(b – 1) – c^{2}(b – 1)

= (b – 1) (ab – c^{2}) Ans.

**Question 20.**

**Solution:**

x^{2} – xz + xy – yz

= x(x – z) + y(x – z)

= (x – z)(x + y)Ans.

**Question 21.**

**Solution:**

6ab – b^{2} + 12ac – 2bc

6ab + 12ac – b^{2} – 2bc

= 6a(b + 2c) – b(b + 2c)

= (b + 2c) (6a – b) Ans.

**Question 22.**

**Solution:**

(x – 2y)^{2} + 4x – 8y

= (x – 2y)^{2} + 4(x – 2y)

= (x – 2y)(x – 2y + 4)Ans.

**Question 23.**

**Solution:**

y^{2} – xy(1 – x) – x^{3}

y^{2} – xy + x^{2}y – x^{2}

= y(y – x) + x^{2} (y – x)

= (y – x)(y + x^{2})Ans.

**Question 24.**

**Solution:**

(ax + by)^{2} + (bx – ay)^{2}

= a^{2}x^{2} + b^{2}y^{2} + 2abxy + b^{2}x^{2} + a^{2}y^{2} – 2abxy

= a^{2}x^{2} + b^{2}y^{2} + b^{2}x^{2} + a^{2}y^{2}

= a^{2}x^{2} + b^{2}x^{2} + a^{2}y^{2} + b^{2}y^{2}

= x^{2}(a^{2} + b^{2}) + y^{2}(a^{2} + b^{2})

= (a^{2} + b^{2}) (x^{2} + y^{2}) Ans.

**Question 25.**

**Solution:**

ab^{2} + (a – 1)b – 1

= ab^{2} + ab – b – 1

= ab(b + 1) – 1(b + 1)

= (b + 1) (ab – 1) Ans.

**Question 26.**

**Solution:**

x^{3} – 3x^{2} + x – 3

= x^{2}(x – 3) + 1(x – 3)

(x – 3)(x^{2} + 1)Ans.

**Question 27.**

**Solution:**

ab (x^{2} + y^{2}) – xy (a^{2} + b^{2})

= abx^{2} + aby^{2} + xya^{2} – xyb^{2}

= abx^{2} – xya^{2} – xyb^{2} + aby2

=ax(bx – ay) – by(bx – ay)

= (bx – ay) (ax – by) Ans.

**Question 28.**

**Solution:**

x^{2} – x (a + 2b) + 2ab

= x^{2} – xa – 2bx + 2ab

= x(x – a) – 2b(x – a)

= (x – a)(x – 2b)

Hope given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7A are helpful to complete your math homework.

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