# How do you rewrite x(x+2)+3(x+2) as an equivalent product of two binomials?

May 30, 2017

$\left(x + 2\right) \left(x + 3\right)$

#### Explanation:

An expression such as $5 x + 15$ can be factored by taking out the common factor of $5$.

$\textcolor{b l u e}{5} x + \textcolor{b l u e}{5} \times 3$

$= \textcolor{b l u e}{5} \left(x + 3\right)$

In the same way the expression can be factored by taking out the common bracket $\left(x + 2\right)$

$x \left(\textcolor{b l u e}{x + 2}\right) + 3 \left(\textcolor{b l u e}{x + 2}\right)$

$= \textcolor{b l u e}{\left(x + 2\right)} \left(x + 3\right)$

May 30, 2017

color(blue)((x+2)(x+3)

#### Explanation:

$x \left(x + 2\right) + 3 \left(x + 2\right)$

$\therefore = {x}^{2} + 2 x + 3 x + 6$

$\therefore = {x}^{2} + 5 x + 6$

:.color(blue)(=(x+2)(x+3)