# How do you factor the expression x^4+216x?

Dec 21, 2015

Factor out the common factor and then look for a familiar form.
Answer is : $x \left(x + 6\right) \left({x}^{2} - 6 x + 36\right) .$

#### Explanation:

Factoring : ${x}^{4} + 216 x$

Always look for a common factor, here it's an $x .$ We get:

$x \left({x}^{3} + 216\right)$

Lucky for us, 216 is a perfect cube:

$x \left({x}^{3} + {6}^{3}\right)$

So it's a sum of cubes and we can use the formula:

$x \left(x + 6\right) \left({x}^{2} - 6 x + {6}^{2}\right) =$

$x \left(x + 6\right) \left({x}^{2} - 6 x + 36\right) .$

You can check that the last quadratic doesn't factor.