# How do you factor 2m + mn + 14 + 7n?

May 13, 2015

We can factor the expression by making groups of 2 terms:

$\left(2 m + m n\right) + \left(14 + 7 n\right)$

$m$ is a common factor to both the terms in the first group, and $7$ is a common factor to both the terms in the second group

$= m \left(2 + n\right) + 7 \left(2 + n\right)$

The binomial $2 + n$ is common to both the terms above:

$= \left(2 + n\right) \left(m + 7\right)$

 = color(green)((n+2)(m+7)

May 13, 2015

The answer is $\left(m + 7\right) \left(2 + n\right)$ .

Problem: Factor $2 m + m n + 14 + 7 n$

There is no GCF, so factor by grouping.

$\left(2 m + m n\right) + \left(14 + 7 n\right)$

Factor out $m$ from the first expression.

$m \left(2 + n\right) + \left(14 + 7 n\right)$

Factor out $7$ from the second expression.

$m \left(2 + n\right) + 7 \left(2 + n\right)$

$\left(2 + n\right)$ is the GCF.

The complete factorization is:

$\left(m + 7\right) \left(2 + n\right)$

Check by using the FOIL method.

$\left(m + 7\right) \left(2 + n\right) = 2 m + m n + 14 + 7 n$