Algebraic Formulae – Expansion of Squares Class 7 Practice Set 53 Answers Solutions Chapter 14
Question 1
Maharashtra Board Solution
Factorize the following expressions: i. p² – q² ii. 4x² – 25y² iii. y² – 4 iv. v. vi. vii. a²b – ab viii. 4x²y – 6x² ix. x. 2x² – 8y²
Solution & Step-by-Step Answer:
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.
Here a = , b =
….[(a² – b²) = (a + b)(a – b)]
v.
Here a = 3x, b =
∴
….[(a² – b²) = (a + b)(a – b)]
vi.
Here a = x, b =
….[(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.
x. 2x² – 8y²
= 2 (x² – 4y²)
= 2 [x² – (2y)²]
= 2(x + 2y)(x – 2y)
….[(a² – b²) = (a + b)(a – b)]