# How do you factor y^3-18y^2+81y?

Jun 12, 2015

${y}^{3} - 18 {y}^{2} + 81 y$
$\textcolor{w h i t e}{\text{XXXX}}$$= y {\left(y - 9\right)}^{2}$

#### Explanation:

${y}^{3} - 18 {y}^{2} + 81 y$
If we extract the obvious common factor from each term
$\textcolor{w h i t e}{\text{XXXX}}$$= y \left({y}^{2} - 18 y + 81\right)$
With a bit of thought the second factor can be seen as a square
$\textcolor{w h i t e}{\text{XXXX}}$$= y \left(y - 9\right) \left(y - 9\right)$