# How do you multiply (2ab+c^2)^2?

Mar 4, 2018

See a solution process below:

#### Explanation:

This is a special form of the quadratic equation:

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

Let $\textcolor{red}{x}$ equal $2 a b$

Let $\textcolor{b l u e}{y}$ equal ${c}^{2}$

Substituting gives:

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

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

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

$4 {a}^{2} {b}^{2} + 4 a b {c}^{2} + {c}^{4}$