Question

How do you factor `64x^4 + xy^3`?

Answer 1

`64x^4+xy^3 = x(4x+y)(16x^2-4xy+y^2)`

Explanation:

The sum of cubes identity can be written:

`a^3+b^3 = (a+b)(a^2-ab+b^2)`

Use this with `a=4x` and `b=y` as follows:

`64x^4+xy^3 = x(64x^3+y^3)`

`color(white)(64x^4+xy^3) = x((4x)^3+y^3)`

`color(white)(64x^4+xy^3) = x(4x+y)((4x)^2-(4x)y+y^2)`

`color(white)(64x^4+xy^3) = x(4x+y)(16x^2-4xy+y^2)`