Students can track their progress and improvement through regular use of OP Malhotra Class 9 Solutions Chapter 4 Factorisation Ex 4(D).

## S Chand Class 9 ICSE Maths Solutions Chapter 4 Factorisation Ex 4(D)

Factorise the following :

Question 1.

x² – 4

Solution:

x² – 4 = (x)² – (2)²

= (x + 2) (x – 2)

Question 2.

y² – 25

Solution:

y² – 25 = (y)² – (5)²

= (y + 5) (y – 5)

Question 3.

a² -1

Solution:

a² – 1 = (a)² – (1)²

= (a + 1) (a – 1)

Question 4.

9z² – 64

Solution:

9z² – 64 = (3z)² – (8)²

= (3z + 8) (3z – 8)

Question 5.

9x² – b²

Solution:

9x² – b²

= (3x)² – (b)²

= (3x + b) (3x – b)

Question 6.

25 – x²y²

Solution:

25 – x²y²

= (5)² – (xy)²

= (5 + xy) (5 – xy)

Question 7.

81a²x² – 49b²y²

Solution:

81a²x² – 49b²y² = (9ax)² – (7by)²

= (9 ax + 7by) (9ax – 7by)

Question 8.

x² – \(\frac { 1 }{ 4 }\)

Solution:

x² – \(\frac { 1 }{ 4 }\) = (x)² – (\(\frac { 1 }{ 2 }\))²

= (x + \(\frac { 1 }{ 2 }\)) (x – \(\frac { 1 }{ 2 }\))

Question 9.

– 25 + \(\frac { 1 }{ 64 }\)b²

Solution:

– 25 + \(\frac { 1 }{ 64 }\) b² = \(\frac { 1 }{ 64 }\) b² – 25

= (\(\frac { 1 }{ 8 }\)b)² – (5)²

= (\(\frac { 1 }{ 8 }\)b + 5) (\(\frac { 1 }{ 8 }\)b – 5)

Question 10.

\(\frac{a^2}{9}-\frac{b^2}{16}\)

Solution:

\(\frac{a^2}{9}-\frac{b^2}{16}=\left(\frac{a}{3}\right)^2-\left(\frac{b}{4}\right)^2\)

= \(\left(\frac{a}{3}+\frac{b}{4}\right)\left(\frac{a}{3}-\frac{b}{4}\right)\)

Question 11.

2.25a² – b²

Solution:

2.25a² – b² = (1.5a)² – (b)²

= (1.5a + b) (1.5a – b)

Question 12.

36a^{8} – 121

Solution:

36a^{8} – 121 = (6a^{4})² – (11)²

= (6a^{4} + 11) (6a^{4} – 11)

Evaluate the following :

Question 13.

54² – 36²

Solution:

(54)² – (36)² = (54 + 36) (54 – 36) {∵ a² – 62 = (a + 6) (a – 6)}

= 90 x 18 = 1620

Question 14.

(3.2)² – (1.8)²

Solution:

(3.2)² – (1.8)² = (3.2 + 1.8) (3.2 – 1.8) {∵ a² – b² = (a + b) (a – b)}

= 5.0 x 1.4 = 7.0 = 7