Question

How do you factor $x^3-8$?

Answer 1

Factorise the expression:

Given expression $x^3-8$.

Rewrite the expression as $x^3-8=x^3-2^3$.

Use the difference of cubes formula $a^3-b^3=(a-b)\left(a^2+ab+b^2\right)$ to factorise the given expression.

$$\begin{gathered} x^3-8=x^3-2^3 \\ \Rightarrow x^3-8=\left(x-2\right)\left(x^2+2·x+2^2\right) \\ \therefore x^3-8=\left(x-2\right)\left(x^2+2x+4\right) \end{gathered}$$

Hence, the factor of $x^3-8$ is $\left(x-2\right)\left(x^2+2x+4\right)$.