# How do you factor 7k(k-3)+4(k-3)?

Jul 21, 2015

$7 k \left(k - 3\right) + 4 \left(k - 3\right) = \left(7 k + 4\right) \left(k - 3\right)$

#### Explanation:

The factor $\textcolor{b l u e}{\left(k - 3\right)}$ occurs in both terms:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{7 k} \textcolor{b l u e}{\left(k - 3\right)}$
$\textcolor{w h i t e}{\text{XXXX}}$and
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{+ 4} \textcolor{b l u e}{\left(k - 3\right)}$

In general, the distributive property tells us that
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{a} \textcolor{b l u e}{\left(c\right)} \textcolor{red}{+ b} \textcolor{b l u e}{\left(c\right)} = \textcolor{red}{\left(a + b\right)} \textcolor{b l u e}{\left(c\right)}$

So, in this case:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{7 k} \textcolor{b l u e}{\left(k - 3\right)} \textcolor{red}{+ 4} \textcolor{b l u e}{\left(k - 3\right)} = \textcolor{red}{\left(7 k + 4\right)} \textcolor{b l u e}{\left(k - 3\right)}$