How do you find the product (3q-5r)^2?

Jul 19, 2017

See a solution process below:

Explanation:

We can use the special case rule:

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

Substituting $\textcolor{red}{\left(3 q\right)}$ for $\textcolor{red}{a}$ and $\textcolor{b l u e}{\left(5 r\right)}$ for $\textcolor{b l u e}{b}$ gives:

${\left(\textcolor{red}{3 q} - \textcolor{b l u e}{5 r}\right)}^{2} \implies {\textcolor{red}{\left(3 q\right)}}^{2} - \left(2 \cdot \textcolor{red}{3 q} \cdot \textcolor{b l u e}{5 r}\right) + {\textcolor{b l u e}{\left(5 r\right)}}^{2} \implies$

#9q^2 - 30qr + 25r^2