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#