# How do you multiply (5 + x)(2x + 10)?

${x}^{2} + 10 x + 25$

#### Explanation:

$\left(5 + x\right) \left(2 x + 10\right)$
$= 10 x + 50 + 2 {x}^{2} + 10 x$
$= 2 {x}^{2} + 10 x + 10 x + 50$
$= 2 {x}^{2} + 20 x + 50$
Divide by 2 to get the simplest form:
$= {x}^{2} + 10 x + 25$

Apr 16, 2018

$2 {x}^{2} + 20 x + 50$

#### Explanation:

$\text{Each term in the second bracket is multiplied by each }$
$\text{term in the first bracket}$

$\Rightarrow \left(\textcolor{red}{5 + x}\right) \left(2 x + 10\right)$

$= \textcolor{red}{5} \left(2 x + 10\right) \textcolor{red}{+ x} \left(2 x + 10\right)$

$= \left(\textcolor{red}{5} \times 2 x\right) + \left(\textcolor{red}{5} \times 10\right) + \left(\textcolor{red}{x} \times 2 x\right) + \left(\textcolor{red}{x} \times 10\right)$

$= \textcolor{b l u e}{10 x} \textcolor{m a \ge n t a}{+ 50} + 2 {x}^{2} \textcolor{b l u e}{+ 10 x}$

$\text{collect like terms}$

$= 2 {x}^{2} + 20 x + 50 \leftarrow \textcolor{red}{\text{in standard form}}$