## RS Aggarwal Class 8 Math Seventh Chapter Factorisation Exercise 7A Solution

## EXERCISE 7A

### Factorise:

**(1) (i) 12x + 15**

= [(3×4) x] + (3 × 5)

= 3(4x + 5)

**(ii) 14m – 21**

= 7 (2m – 3)

**(iii) 9n – 12n ^{2}**

= 3n (3 – 4n)

**(2) (i) 16a ^{2} – 24ab**

= 8a (2a – 3b)

**(ii) 15ab ^{2} – 20a^{2}b**

= 5ab (3b – 4a)

**(iii) 12x ^{2}y^{3} – 21x^{3}y^{2}**

= 3x^{2}y^{2} (4y – 7x)

**(3) (i) 24x ^{3} – 36x^{2}y**

= 12x^{2} (2x – 3y)

**(ii) 10x ^{3} – 15x^{2}**

= 5x^{2} (2x – 3)

**(iii) 36x ^{3}y – 60x^{2}y^{3}z**

= 12x^{2}y (3x – 5y^{2}z)

**(4) (i) 9x ^{3} – 6x^{2} + 12x**

= 3x (3x^{2} – 2x + 4)

**(ii) 8x ^{2} – 72xy + 12x**

= 4x (2x – 18y + 3)

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

= 9a^{2}b^{2} (2ab – 3b + 4a)

**(5) (i) 14x ^{3} + 21x^{4}y – 28x^{2}y^{2}**

= 7x^{2} (2x + 3x^{2}y – 4y^{2})

**(ii) – 5 – 10t + 20t ^{2}**

= – 5 (1 + 2y – 4t^{2})

**(6) (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)

**(7) 6a(a – 2b) + 5b(a – 2b)**

= (a – 2b) (6a + 5b)

**(8) x ^{3}(2a – b) + x^{2} (2a – b)**

= (2a – b) (x^{3} + x^{2})

= x^{2} (2a – b) (x + 1)

**(9) 9a(3a – 5b) – 12a ^{2}(3a – 5b)**

= (3a – 5b) [3a(3 – 4a)]

= 3a (3a – 5b) (3 – 4a)

**(10) (x + 5) ^{2} – 4(x + 5)**

= (x + 5) [(x + 5) – 4]

= (x + 5) (x + 1)

**(11) 3(a – 2b) ^{2} – 5(a – 2b)**

= (a – 2b) (3a – 6b – 5)

**(12) 2a + 6b – 3(a + 3b) ^{2}**

= 2(a + 3b) – 3(a + 3b)^{2}

= (a + 3b) (2 – 3a – 9b)

**(13) 16(2p – 3q) ^{2} – 4(2p – 3q)**

= (2p – 3q) (32p – 48q – 4)

= 4 (2p – 3q) (8p – 12q – 1)

**(14) x(a – 3) + y(3 – a)**

= x(a – 3) – y(a – 3)

= (a – 3) (x – y)

**(15) 12(2x – 3y) ^{2} – 16(3y – 2x)**

= 12(2x – 3y)^{2} + 16(2x – 3y)

= (2x – 3y) (24x – 36y + 16)

= 4 (2x – 3y) (6x – 9y + 4)

**(16) (x + y) (2x + 5) – (x + y) (x + 3)**

= (x + y) [(2x + 5) – (x + 3)]

= (x + y) (2x + 5 – x – 3)

= (x + y) (x + 2)

**(17) ar + br + at + bt**

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

= (a + b) (r + t)

**(18) x^{2} – ax – bx + ab**

= x (x – a) – b (x – a)

= (x – a) (x – b)

**(19) ab^{2} – bc^{2} – ab + c^{2}**

= b (ab – c^{2}) – 1(ab – c^{2})

= (ab – c^{2}) (b – 1)

**(20) x ^{2} – xz + xy – yz**

= x (x – z) + y (x – z)

= (x – z) (x + y)

**(21) 6ab – b ^{2} + 12ac – 2bc**

= b(6a – b) + 2c (6a – b)

= (6a – b) (b + 2c)

**(22) (x – 2y) ^{2} + 4x – 8y**

= (x – 2y) (x – 2y) + 4(x – 2y)

= (x – 2y) (x – 2y + 4)

**(23) y ^{2} – xy(1 – x) – x^{3}**

= y^{2} – xy + x^{2}y – x^{3}

= y(y – x) + x^{2}(y – x)

= (y – x) (y + x^{2})

**(24) (ax + by) ^{2} + (bx – ay)^{2}**

= [(ax)^{2} + 2axby + (by)^{2}] + [(bx)^{2} – 2bxay + (ay)^{2}]

= a^{2}x^{2} + 2axby + b^{2}y^{2} + b^{2}x^{2} – 2axby + 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})

**(25) ab ^{2} + (a – 1) b – 1**

= ab^{2} + ab – b – 1

= ab(b + 1) – 1(b + 1)

= (b + 1) (ab – 1)

**(26) x ^{3} – 3x^{2} + x – 3**

= x^{2}(x – 3) + 1 (x – 3)

= (x – 3) (x^{2} + 1)

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

= abx^{2} + aby^{2} – a^{2}xy – b^{2}xy

= abx^{2 }– a^{2}xy – b^{2}xy + aby^{2}

= ax (bx – ay) – by (bx – ay)

= (bx – ay) (ax – by)

**(28) x ^{2} – x(a + 2b) + 2ab**

= x^{2} – ax – 2bx + 2ab

= x(x – a) – 2b (x – a)

= (x – a) (x – 2b)

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