Question

Factorize the following expressions :

i. p² – q²

ii. 4x² – 25y²

iii. y² – 4

iv. p² − \(\frac{1}{25}\)

v. 9x² − \(\frac{1}{25}\) y²

Answer 1

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 - \(\frac{1}{25}\)

Here a = \(\frac{1}{25},\) b = \(\frac{1}{5}\)