Question

How do you factor $({\mathrm{x}}^3-64)$?

Answer 1

Factorize the given expression:

Given polynomial $({\mathrm{x}}^3-64)$ can also be written as ${\mathrm{x}}^3-4^3$

Now, ${\mathrm{x}}^3-4^3=\left(\mathrm{x}-4\right)\left({\mathrm{x}}^2+4\mathrm{x}+16\right)$ $\left[{\mathrm{a}}^3-{\mathrm{b}}^3=\left(\mathrm{a}-\mathrm{b}\right)\left({\mathrm{a}}^2+\mathrm{ab}+{\mathrm{b}}^2\right)\right]$

Hence, factorization of $({\mathrm{x}}^3-64)$ is $\left(\mathrm{x}-4\right)\left({\mathrm{x}}^2+4\mathrm{x}+16\right)$.