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

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

Maharashtra state board textbooks

Std 7 Maths Practice Set 53 Solutions Answers

Question 1.
Factorize the following expressions:
i. p² – q²
ii. 4x² – 25y²
iii. y² – 4
iv. p2−125
v. 9x2−116y2
vi. x2−1x2
vii. a²b – ab
viii. 4x²y – 6x²
ix. 12y2−8z2
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. p2−125
Here a = 125, b = 15
p2−(15)2=(p+15)(p−15)
….[(a² – b²) = (a + b)(a – b)]

v. 9x2−116y2
Here a = 3x, b = 14y
∴(3x)2−(14y)2=(3x+14y)(3x−14y)
….[(a² – b²) = (a + b)(a – b)]

vi. x2−1x2
Here a = x, b = 1x
x2−(1x)2=(x+1x)(x−1x)
….[(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. 12y2−8z2

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