Factorize the following expressions: i. p2 – q2ii. 4x2 – 25y2 i

1.	Factorize the following expressions: i. p2 – q2ii. 4x2 – 25y2 iii. y2 – 4 iv. P2 - 1/25v. 9x2 - 1/16y2
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 P² - 1/25 Here a = 1/25, b = 1/5 P² - (1/5)² = (P + 1/5) (p - 1/5) ... [(a²- b² ) = (a + b)(a - b)] v. 9x² - 1/16y² Here a = 3x, b= 1/4y ∴ (3x)² - (1/4y)² = (3x + 1/4y)(3x - 1/4y) ….[(a² – b²) = (a + b)(a – b)]

Factorize the following expressions: i. p2 – q2ii. 4x2 – 25y2 iii. y2 – 4 iv. P2 - 1/25v. 9x2 - 1/16y2

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 P² - 1/25

Here a = 1/25, b = 1/5

P² - (1/5)² = (P + 1/5) (p - 1/5) ... [(a²- b² ) = (a + b)(a - b)]

v. 9x² - 1/16y²

Here a = 3x, b= 1/4y

∴ (3x)² - (1/4y)² = (3x + 1/4y)(3x - 1/4y) ….[(a² – b²) = (a + b)(a – b)]