Question

Factor:


(m+2)^2−(m+2)+mn·(n+2)+2n(n+2)

Answer 1

ANSWER

`{(m + 2)}( {n}^(2) + 2n + m + 1)`

Step-by-step explanation

The given expression is


`{(m + 2)}^(2) - (m + 2) + mn(n + 2) + 2n(n + 2)`

We factor to get,


`= {(m + 2)}(m + 2 - 1) +n (n + 2) (m+ 2)`

This implies that,


`= {(m + 2)}(m + 1) +n (n + 2) (m+ 2)`

We factor further to obtain,


`= {(m + 2)}((m + 1) +n (n + 2))`

or


`= {(m + 2)}( {n}^(2) + 2n + m + 1)`