Question

Factorize the following expressions:

i. x² - 1/x²

ii. a² b - ab

iii. 4x² y - 6x²

iv. 1/2y² - 8z²

v. 2x² - 8y²

Answer 1

i. x² - 1/x²

Here a = x, b = 1/x

x²  - (1/x)²  = (x + 1/x)(x - 1/x) ... [(a² - b² ) = (a + b)(a - b)]

ii. a² b - ab

= a (ab - b)

= ab (a -1) 

iii. 4x² y - 6x²

= 2(2x² y – 3x² ) 

= 2x² (2y – 3)

iv. 1/2y² - 8z²

v. 2x² - 8y²

= 2 (x²  – 4y² ) 

= 2 [x²  – (2y)² ] 

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