Question

Factorise: i. a^4 − (a− b)^4

Answer 1

Answer:

$a {}^{4} - (a - b) {}^{4} \\ \\ = (a {}^{2} ) {}^{2} - ((a - b) {}^{2} ) {}^{2} \\ \\ =( a {}^{2} + (a - b) {}^{2} )(a {}^{2} - ( a- b) {}^{2} ) \\ \\ = (a {}^{2} + a {}^{2} + b {}^{2} - 2ab)(a + a - b)(a -( a - b)) \\ \\ = (2a {}^{2} + b {}^{2} - 2ab)(2a - b)(a - a + b) \\ \\ = b(2a {}^{2} + b {}^{2} - 2ab)(2a - b) \\ \\ \\ formula \: \: \: - \: \: (x {}^{2} - y {}^{2} ) = (x + y)(x - y) \\ \\ \: \: (x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

Answer 2

break it into =(a²)²-((a-b) ²)²

=(a²-(a-b)²) (a²+(a-b)²)

=(a-(a-b)) (a+(a-b))(a²+(a-b) ²)

=(a-a+b)(a+a-b) (a²+a²+b²+2ab)

=b(2a-b) (2a²+b²+2ab) ans...