# How do you find the product of (7x^2 + 5y + 7) (y + 5) ?

Oct 24, 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.

$\left(\textcolor{red}{7 {x}^{2}} + \textcolor{red}{5 y} + \textcolor{red}{7}\right) \left(\textcolor{b l u e}{y} + \textcolor{b l u e}{5}\right)$ becomes:

$\left(\textcolor{red}{7 {x}^{2}} \times \textcolor{b l u e}{y}\right) + \left(\textcolor{red}{7 {x}^{2}} \times \textcolor{b l u e}{5}\right) + \left(\textcolor{red}{5 y} \times \textcolor{b l u e}{y}\right) + \left(\textcolor{red}{5 y} \times \textcolor{b l u e}{5}\right) + \left(\textcolor{red}{7} \times \textcolor{b l u e}{y}\right) + \left(\textcolor{red}{7} \times \textcolor{b l u e}{5}\right)$

$7 {x}^{2} y + 35 {x}^{2} + 5 {y}^{2} + 25 y + 7 y + 35$

We can now combine like terms:

$7 {x}^{2} y + 35 {x}^{2} + 5 {y}^{2} + \left(25 + 7\right) y + 35$

$7 {x}^{2} y + 35 {x}^{2} + 5 {y}^{2} + 32 y + 35$