Question

How do I factor x^3-64

Answer 1

Given the expression:

`x^3-64`

The above expression can be rewritten as

`(x^3-4^3)`

To factor the expression, we apply the difference cubes formula.

From the difference cubes formula:

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

In this case,

`y=4`

Thus, we have

`\begin{gathered} (x^3-64)=(x^3-4^3) \\ =(x-4)(x^2+4x+4^2) \\ =(x-4)(x^2+4x+16) \end{gathered}`

Hence, we have

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