# How do you multiply (ab + xy)(7ab + 9xy)?

Jul 5, 2017

See a solution process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{a b} + \textcolor{red}{x y}\right) \left(\textcolor{b l u e}{7 a b} + \textcolor{b l u e}{9 x y}\right)$ becomes:

$\left(\textcolor{red}{a b} \times \textcolor{b l u e}{7 a b}\right) + \left(\textcolor{red}{a b} \times \textcolor{b l u e}{9 x y}\right) + \left(\textcolor{red}{x y} \times \textcolor{b l u e}{7 a b}\right) + \left(\textcolor{red}{x y} \times \textcolor{b l u e}{9 x y}\right)$

$7 {a}^{2} {b}^{2} + 9 a b x y + 7 a b x y + 9 {x}^{2} {y}^{2}$

We can now combine like terms:

$7 {a}^{2} {b}^{2} + \left(9 + 7\right) a b x y + 9 {x}^{2} {y}^{2}$

$7 {a}^{2} {b}^{2} + 16 a b x y + 9 {x}^{2} {y}^{2}$