# How do you find the product of (6x + 7)^2?

Mar 6, 2018

See a solution process below:

#### Explanation:

This is a special form of the quadratic:

${\left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right)}^{2} = \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) = {\textcolor{red}{a}}^{2} + 2 \textcolor{red}{a} \textcolor{b l u e}{b} + {\textcolor{b l u e}{b}}^{2}$

Let:

$a = 6 x$ and $b = 7$

Substituting gives:

${\left(\textcolor{red}{6 x} + \textcolor{b l u e}{7}\right)}^{2} \implies$

$\left(\textcolor{red}{6 x} + \textcolor{b l u e}{7}\right) \left(\textcolor{red}{6 x} + \textcolor{b l u e}{7}\right) \implies$

${\textcolor{red}{\left(6 x\right)}}^{2} + \left(2 \times \textcolor{red}{6 x} \times \textcolor{b l u e}{7}\right) + {\textcolor{b l u e}{7}}^{2} \implies$

$36 {x}^{2} + 84 x + 49$