Question

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

Answer 1

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

Explanation:

Both `x^3` and `64=4^3` are perfect squares.

So we can use the sum of cubes identity:

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

with `a=x` and `b=4` as follows:

`x^3+64`

`=x^3+4^3`

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

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