# How do you simplify (x - 5)(x + 2)?

May 1, 2018

${x}^{2} - 3 x - 10$

#### Explanation:

Open the bracket and multiply the two factors and then add the similar values or variables:
$\left(x - 5\right) \left(x + 2\right)$
${x}^{2} + 2 x + \left(- 5\right) x + \left(- 10\right)$
${x}^{2} + 2 x - 5 x - 10$
${x}^{2} - 3 x - 10$

May 1, 2018

${x}^{2} - 3 x - 10$

#### Explanation:

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

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

$= \textcolor{red}{x} \left(x + 2\right) \textcolor{red}{- 5} \left(x + 2\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

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

$= {x}^{2} \textcolor{m a \ge n t a}{+ 2 x} \textcolor{m a \ge n t a}{- 5 x} \textcolor{b l u e}{- 10} \leftarrow \text{collect like terms}$

$= {x}^{2} - 3 x - 10$