# Maharashtra Board Class 7 Maths Solutions Chapter 14 Algebraic Formulae – Expansion of Squares Practice Set 53

## Maharashtra State Board Class 7 Maths Solutions Chapter 14 Algebraic Formulae – Expansion of Squares Practice Set 53

Question 1.
Factorize the following expressions:
i. p² – q²
ii. 4x² – 25y²
iii. y² – 4
iv. $$\mathrm{p}^{2}-\frac{1}{25}$$
v. $$9 x^{2}-\frac{1}{16} y^{2}$$
vi. $$x^{2}-\frac{1}{x^{2}}$$
vii. a²b – ab
viii. 4x²y – 6x²
ix. $$\frac{1}{2} y^{2}-8 z^{2}$$
x. 2x² – 8y²
Solution:
i. p² – q²
Here, a = p, b = q
∴ p² – q² = (p + q)(p – q)
….[(a² – b²) = (a + b)(a – b)]

ii. 4x² – 25y²
= (2x)² – (5y)²
Here, a = 2x, b = 5y
∴ (2x)² – (5y)² = (2x + 5y)(2x – 5y)
….[(a² – b²) = (a + b)(a – b)]

iii. y² – 4
= y² – 2²
Here, a = y, b = 2
∴ y² – 2² = (y + 2)(y – 2)
….[(a² – b²) = (a + b)(a – b)]

iv. $$\mathrm{p}^{2}-\frac{1}{25}$$
Here a = $$\frac { 1 }{ 25 }$$, b = $$\frac { 1 }{ 5 }$$
$$p^{2}-\left(\frac{1}{5}\right)^{2}=\left(p+\frac{1}{5}\right)\left(p-\frac{1}{5}\right)$$
….[(a² – b²) = (a + b)(a – b)]

v. $$9 x^{2}-\frac{1}{16} y^{2}$$
Here a = 3x, b = $$\frac { 1 }{ 4 }y$$
∴$$(3 x)^{2}-\left(\frac{1}{4} y\right)^{2}=\left(3 x+\frac{1}{4} y\right)\left(3 x-\frac{1}{4} y\right)$$
….[(a² – b²) = (a + b)(a – b)]

vi. $$x^{2}-\frac{1}{x^{2}}$$
Here a = x, b = $$\frac { 1 }{ x }$$
$$x^{2}-\left(\frac{1}{x}\right)^{2}=\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)$$
….[(a² – b²) = (a + b)(a – b)]

vii. a²b – ab
= a (ab – b)
= ab (a – 1)

viii. 4x²y – 6x²
= 2 (2x²y – 3x²)
= 2x² (2y – 3)

ix. $$\frac{1}{2} y^{2}-8 z^{2}$$

x. 2x² – 8y²
= 2 (x² – 4y²)
= 2 [x² – (2y)²]
= 2(x + 2y)(x – 2y)
….[(a² – b²) = (a + b)(a – b)]