Question 1.

Factorize the following expressions:

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)]

vii. a²b – ab

= a (ab – b)

= ab (a – 1)

viii. 4x²y – 6x²

= 2 (2x²y – 3x²)

= 2x² (2y – 3)

ix. 12*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)]