Question

factorise 16x^4-625y^4​

Answer 1

16x⁴ - 625y⁴

= (4x²)² - (25y²)²

= (4x² - 25y²)(4x² + 25y²)

= [(2x)² - (5y)²](4x² + 25y²)

= (2x - 5y)(2x + 5y)(4x² + 25y²).

Answer 2

16x⁴ - 625y⁴ = (2x - 5y)(2x + 5y)(4x² + 25y²)

Given :

The expression 16x⁴ - 625y⁴

To find :

Factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is 16x⁴ - 625y⁴

Step 2 of 2 :

Factorise the expression

$\sf 16 {x}^{4} - 625 {y}^{4}$

$\sf = {(4 {x}^{2} )}^{2} - {(25 {y}^{2} )}^{2}$

$\sf =(4 {x}^{2} + 25 {y}^{2} )(4 {x}^{2} - 2 5 {y}^{2} )$

$\sf =(4 {x}^{2} + 25 {y}^{2} ) \{ {(2x)}^{2} - {(5y)}^{2} ) \}$

$\sf =(4 {x}^{2} + 25 {y}^{2} ) (2x + 5y)(2x - 5y)$

$\sf =(2x - 5y)(2x + 5y)(4 {x}^{2} + 25 {y}^{2} )$

∴ 16x⁴ - 625y⁴ = (2x - 5y)(2x + 5y)(4x² + 25y²)