How do you multiply (4c+9d)^2?

Aug 13, 2017

See a solution process below:

Explanation:

We can use this rule for multiplication to multiply the expression:

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

Substituting $\textcolor{red}{4 c}$ for $\textcolor{red}{x}$ and $\textcolor{b l u e}{9 d}$ for $\textcolor{b l u e}{y}$ gives:

${\left(\textcolor{red}{4 c} + \textcolor{b l u e}{9 d}\right)}^{2} \implies {\left(\textcolor{red}{4 c}\right)}^{2} + \left(2 \cdot \textcolor{red}{4 c} \cdot \textcolor{b l u e}{9 d}\right) + {\left(\textcolor{b l u e}{9 d}\right)}^{2} \implies$

$16 {c}^{2} + 72 c d + 81 {d}^{2}$