Question

How do you factor `2x^4-32y^4`?

Answer 1

`2x^4-32y^4 = 2(x-2y)(x+2y)(x^2+4y^2)`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Hence we find:

`2x^4-32y^4 = 2(x^4-16y^4)`

`color(white)(2x^4-32y^4) = 2((x^2)^2-(4y^2)^2)`

`color(white)(2x^4-32y^4) = 2(x^2-4y^2)(x^2+4y^2)`

`color(white)(2x^4-32y^4) = 2(x^2-(2y)^2)(x^2+4y^2)`

`color(white)(2x^4-32y^4) = 2(x-2y)(x+2y)(x^2+4y^2)`