Nootan solutions for Mathematics [English] Class 9 ICSE chapter 4 - Factorisation [Latest edition]

Factorise the following:

bx – by

Factorise the following:

ax – ay + az

Factorise the following:

2x² + 7x – 3xz

Factorise the following:

x³y⁴ – 4x⁴y³

Factorise the following:

πr² – 2πr

Factorise the following:

x²yz + xyz² + xy²z

Factorise the following:

42a²bc⁴ – 56a³b²c³

Factorise the following:

a²(x + y) + b²(x + y)

Factorise the following:

p(x² + 1) – 2q(x² + 1)

Factorise the following:

20(x – y)² – 30(x – y)³

Factorise the following:

5(a – 2b)³ + 15(a – 2b)² – 25(a – 2b)

Factorise the following:

16(3x + y)³ – 24(3x + y)

Factorise the following:

a(x² + y² – z²) – b(–x² – y² + z²)

Factorise the following:

p(a² + a – b) + q(b – a – a²)

Factorise the following:

p²(q² + r²) + p(q² + r²) + (q² + r²)²

Factorise the following:

ab + bc + ad + cd

Factorise the following:

x² + x + bx + b

Factorise the following:

ax + ay + az + bx + by + bz

Factorise the following:

ax² + bx² + ay² + by²

Factorise the following:

x³ – 3x² – 2x + 6

Factorise the following:

x⁴ + 2x³ + 3x² + 6x

Factorise the following:

1 – a – b + ab

Factorise the following:

2ax – 4ay – bx + 2by

Factorise the following:

x(x + 2y – z) – 2yz

Factorise the following:

x² + x(1 + p) + p

Factorise the following:

x² – x(3a + 2b) + 6ab

Factorise the following:

`x^2 + 1/x^2 - 2 - 3x + 3/x`

Factorise the following:

x² + y² + 2xy – 2x – 2y

Factorise the following:

(ax – by)² – (bx – ay)²

Factorise the following:

x² + y² – 2(xy – xz + yz)

Factorise the following:

`x^2 - (a/b + b/a)x + 1`

Factorise the following:

ab(x² + y²) – xy(a² + b²)

Factorise the following:

`x^2 + (a + 1/a)x + 1`

Factorise the following:

4x² – y²

Factorise the following:

x² – 9y²

Factorise the following:

16x² – 9y²

Factorise the following:

96x² – 216y²

Factorise the following:

4x² – 25

Factorise the following:

120 – 30х²

Factorise the following:

5x³ – 80x

Factorise the following:

(a + b)² – 9

Factorise the following:

8 – 2(x – 1)²

Factorise the following:

4 – (x – y)²

Factorise the following:

36x² – 4(y – z)²

Factorise the following:

(x – 4) (x + 4) + 7

Factorise the following:

x² – 4y² – 2x + 4y

Factorise the following:

x + 3y – x² + 9y²

Factorise the following:

9x² – 4(x + y)²

Factorise the following:

x² – 2xy + y² – 16

Factorise the following:

(x + y)³ – x – у

Factorise the following:

x² – 25y² + 2x – 10y

Factorise the following:

4x² – a² + 2a – 1

Factorise the following:

9 – x² + 2xy – y²

Factorise the following:

(1 – x²) (1 – y²) + 4xy

Factorise the following:

(a² – b²)(c² – d²) – 4abcd

Factorise the following:

x⁴ + 4

Factorise the following:

x⁴ + x² + 1

Factorise the following:

4x⁴ + y⁴ + 3x²y²

Factorise the following:

x⁴ – 14x² + 1

Factorise the following:

`x^2 + 1/x^2 - 14`

Express the following as the difference of two squares: 

(x² + x + 1) (x² – x + 1)

Express the following as the difference of two squares: 

(x² + 5x + 6) (x² – 5x – 6)

Factorise the following:

x² + 3x + 2

Factorise the following.

x² + 9x + 20

Factorise the following:

x² – 8x + 15

Factorise the following:

x² – 27x + 180

Factorise the following:

x² + 10x – 24

Factorise the following:

x² – 5x – 50

Factorise the following:

x² – 18x – 63

Factorise the following:

3x² + 13x + 14

Factorise the following:

3x² + 7x + 2

Factorise the following:

6y² + 19y + 15

Factorise the following:

15 – 4х – 4x²

Factorise the following:

11 – 8x – 3x²

Factorise the following:

x³ – 5x² + 6x

Factorise the following:

7x² + 10xy – 8y²

Factorise the following:

`3sqrt(2)x^2 - 11x + 4sqrt(2)`

Factorise the following:

`2sqrt(3)x^2 + x - 5sqrt(3)`

Factorise the following:

`x^2 + (11x)/6 - 5/3`

Factorise the following:

`x^2 + 7/6 x - 5/6`

Factorise the following:

x(2x – y) – y²

Factorise the following:

x(6x – 7) – 5

Factorise the following:

12(x + y)² – x – y – 1

Factorise the following:

(3x – 2y)² – 6(3x – 2y) – 135

Factorise the following:

x⁴ – 5x² + 4

Factorise the following:

x⁴ – 20x²y² + 64y⁴

Factorise the following:

(x² – x)² – 26(x² – x) + 120

Factorise the following:

(x² + 2x)² – 18(x² + 2x) + 45

Factorise the following:

(2x² – x) (2x² – x – 4) + 3

Factorise the following:

x³ + 64

Factorise the following:

27x³ + 8

Factorise the following:

x³ + 8y³

Factorise the following:

8x³ + 125y³

Factorise the following:

x³ – 8

Factorise the following:

125x³ – 64

Factorise the following:

x⁵ – 64x²

Factorise the following:

`64x^3 - 27/y^3`

Factorise the following:

`x^3/8 - y^3`

Factorise the following:

`27x^3 + 1/(27x^3)`

Factorise the following:

xy⁷ – x⁷y

Factorise the following:

64x⁴ – 1000x

Factorise the following:

(2x + y)³ + (x + y)³

Factorise the following:

(2x + 3y)³ – (x + y)³

Factorise the following:

8x³ – (x – у)³

Factorise the following:

x⁶ – 63x³ – 64

Factorise the following:

x⁹ + y⁹

Factorise the following:

x⁶ – 7x³ – 8

Factorise the following:

x⁶ – 19x³ – 196

Factorise the following:

x³ + 3x²y + 3xy² + 9y³

Factorise the following:

x³ + 8y³ + x² – 4y²

Factorise the following:

4x² – 9y² – 8x³ + 27y³

x² – y² is equal to ______.

x³ – y³ is equal to ______.

x² + 9x + 20 is equal to ______.

(17)² – (13)² is equal to ______.

Factors of x⁴ + 4y⁴ are ______.

Factors of (3 – x – 4x²) are ______.

Factors of x³ – 3x² – x + 3 are ______.

One factor of (x – y)³ – (x³ – y³) is ______.

Factors of 9x² – 16y² are ______.

Factors of `x^2 + (a + 1/a)x + 1` are ______.

(i) x² – y² + 2xy = (x + y)²

(ii) `x^2 - (a + 1/a)x + 1 = (x - a)(x + 1/a)`

(i) 8x³ – y³ = (2x – y) (4x² + 2xy + y²)

(ii) 16x² – 9y² = (4x – 3y) (4x + 3y)

(i) 4x⁴ + y⁴ = (2x² + y² + 2xy) (2x² + y² – 2xy)

(ii) x² – 7x – 8 = (x + 8) (x – 1)

(i) `4x^2 - 5sqrt(2)x - 7 = (2sqrt(2)x + 7)(sqrt(2)x - 1)`

(ii) x² + x + px + p = (x + 1)(x + p)