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

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Answer 1 · 2015-05-13T06:29:50

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

$(2m + mn) + (14 + 7n)$

$m$ 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

$= m(2+n) + 7(2+n)$

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

$= (2+n)(m+7)$

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

Answer 2 · 2015-05-13T06:40:10

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

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

There is no GCF, so factor by grouping.

$(2m+mn)+(14+7n)$

Factor out $m$ from the first expression.

$m(2+n)+(14+7n)$

Factor out $7$ from the second expression.

$m(2+n)+7(2+n)$

$(2+n)$ is the GCF.

The complete factorization is:

$(m+7)(2+n)$

Check by using the FOIL method.

$(m+7)(2+n)=2m+mn+14+7n$

How do you factor 2m + mn + 14 + 7n2m + mn + 14 + 7n?