# How do you factor y= 4x^2 – 36x+ 81  ?

Dec 26, 2015

$4 {x}^{2} - 36 x + 81 = {\left(2 x - 9\right)}^{2}$

#### Explanation:

We can recognise this as a perfect square trinomial.

In general ${\left(a \pm b\right)}^{2} = {a}^{2} \pm 2 a b + {b}^{2}$

In our example notice that $4 {x}^{2} = {\left(2 x\right)}^{2}$ and $81 = {9}^{2}$ are both perfect squares, so the question is, if we let $a = 2 x$ and $b = 9$ then does $\pm 2 a b$ match the middle term $- 36 x$. Yes with a minus sign.

Hence:

$4 {x}^{2} - 36 x + 81 = {\left(2 x - 9\right)}^{2}$