Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$ 16x^4- 625y^4$
$ 16x^4- 625y^4$
✓
Answer
$16x^4- 625y^4$
$= (4x^2)^2- (25y^2)^2$
$= (4x^2+ 25y^2)(4x^2- 25y^2)$
$= (4x^2+ 25y^2)[(2x)^2- (5y)^2]$
$= (4x^2+ 25y^2)(2x + 5y)(2x - 5y)$
$= (4x^2)^2- (25y^2)^2$
$= (4x^2+ 25y^2)(4x^2- 25y^2)$
$= (4x^2+ 25y^2)[(2x)^2- (5y)^2]$
$= (4x^2+ 25y^2)(2x + 5y)(2x - 5y)$
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