Question

Factorise the following using the identity a² – b² = (a + b)(a – b).

(x + y)⁴ – (x – y)⁴

Answer 1

We have,

(x + y)⁴ – (x – y)⁴ = [(x + y²]² – [(x – y)²]²

= [(x + y)² + (x – y)²][(x + y)² – (x – y²)]

= (x² + y² + 2xy + x² + y² – 2xy)(x + y + x – y)(x + y – x + y)

= (2x² + 2y²)(2x)(2y)

= 2(x² + y²)(2x)(2y)

= 8xy(x² + y²)