ANSWER
[tex]{(m + 2)}( {n}^{2} + 2n + m + 1)[/tex]
EXPLANATION
The given expression is
[tex] {(m + 2)}^{2} - (m + 2) + mn(n + 2) + 2n(n + 2)[/tex]
We factor to get,
[tex] = {(m + 2)}(m + 2 - 1) +n (n + 2) (m+ 2)[/tex]
This implies that,
[tex] = {(m + 2)}(m + 1) +n (n + 2) (m+ 2)[/tex]
We factor further to obtain,
[tex] = {(m + 2)}((m + 1) +n (n + 2))[/tex]
or
[tex] = {(m + 2)}( {n}^{2} + 2n + m + 1)[/tex]
