Question

Factorise the following :
i.(x+y)^ 4 -(x-y)^4

Answer 1

Answer:

Use this formula: a^2 - b^2 = (a + b)(a - b), called difference of squares

x^4 - (x - y)^4

= (x^2 + (x - y)^2)(x^2 - (x - y)^2)

= (x^2 + (x - y)^2)(x + (x - y))(x - (x - y))

= (x^2 + x^2 - 2xy + y^2)(2x - y)(-y)

= (2x^2 - 2xy + y^2)(y - 2x)(y)