# How do you factor y= x^3 + 9x^2 + 27x + 27 ?

Dec 2, 2015

$y = {x}^{3} + 9 {x}^{2} + 27 x + 27 = {\left(x + 3\right)}^{3}$

#### Explanation:

Notice that ${x}^{3}$ is a perfect cube and $27 = {3}^{3}$ is also a perfect cube.

So try ${\left(x + 3\right)}^{3}$ to see if the middle two terms match.

In general ${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$, so:

${\left(x + 3\right)}^{3} = \left({x}^{3}\right) + 3 \left({x}^{2}\right) \left(3\right) + 3 \left(x\right) \left({3}^{2}\right) + \left({3}^{3}\right)$

$= {x}^{3} + 9 {x}^{2} + 27 x + 27$