Question

How do I factor x^3-64

Answer 1

Solution:

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

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