OP Malhotra Class 9 Maths Solutions Chapter 4 Factorisation Ex 4(D)

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.
36a⁸ – 121
Solution:
36a⁸ – 121 = (6a⁴)² – (11)²
= (6a⁴ + 11) (6a⁴ – 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