# How do you determine whether 36x^2-84x+49 is a perfect square trinomial?

May 27, 2017

${\left(6 x - 7\right)}^{2}$

#### Explanation:

$\text{note that } 36 {x}^{2} = {\left(6 x\right)}^{2}$

$\text{and } 49 = {7}^{2} = {\left(- 7\right)}^{2}$

$\Rightarrow 36 {x}^{2} - 84 x + 49$

$= \left(6 x - 7\right) \left(6 x - 7\right)$

$= {\left(6 x - 7\right)}^{2} \leftarrow \textcolor{red}{\text{ a perfect square}}$