# How do you multiply (2r+3)(7r+7)?

Jun 6, 2017

See below.

#### Explanation:

$\left(2 r + 3\right) \left(7 r + 7\right)$

$= 7 r \left(2 r + 3\right) + 7 \left(2 r + 3\right)$

$= 14 {r}^{2} + 21 r + 14 r + 21 \text{ }$ (Collect like terms)

$= 14 {r}^{2} + 35 r + 21 \text{ }$ (Add like terms, which are $27 r + 14 r$)

Jun 6, 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.

$\left(\textcolor{red}{2 r} + \textcolor{red}{3}\right) \left(\textcolor{b l u e}{7 r} + \textcolor{b l u e}{7}\right)$ becomes:

$\left(\textcolor{red}{2 r} \times \textcolor{b l u e}{7 r}\right) + \left(\textcolor{red}{2 r} \times \textcolor{b l u e}{7}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{7 r}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{7}\right)$

$14 {r}^{2} + 14 r + 21 r + 21$

We can now combine like terms:

$14 {r}^{2} + \left(14 + 21\right) r + 21$

$14 {r}^{2} + 35 r + 21$