# How do you find the product (3a^2+7b)(3a^2-7b)?

Aug 29, 2017

See a solution process below:

#### Explanation:

This is a special case quadratic:

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

Let $\textcolor{red}{x} = \textcolor{red}{3 {a}^{2}}$ and let $\textcolor{b l u e}{b} = \textcolor{b l u e}{- 7 b}$

Substituting gives:

$\left(\textcolor{red}{3 {a}^{2}} + \textcolor{b l u e}{- 7 b}\right) \left(\textcolor{red}{3 {a}^{2}} - \textcolor{b l u e}{- 7 b}\right) = {\textcolor{red}{\left(3 {a}^{2}\right)}}^{2} - {\textcolor{b l u e}{\left(- 7 b\right)}}^{2} = 9 {a}^{4} - 49 {b}^{2}$