Question

How do you factor completely `64-x^3`?

Answer 1

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

Explanation:

The difference of cubes identity can be written:

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

Note both `64=4^3` and `x^3` are perfect cubes.

So we find:

`64-x^3 = 4^3-x^3`

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

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