Factor out $(m+2)$ in the following equation $(m+1)(m+2)+2(m+2)$

Question

$(m+1)(m+2)+2(m+2)$

I really needed hints here, I am thinking to start at first two paragraphs and so on. Is my thought correct?

Hints will be much appreciated.

Answer 1

Perhaps it would make it more clear if you substitute in $u=m+2$ and then factor:

$$(m+1)u+2u$$

$$=u((m+1)+2)$$

$$=u(m+3)=(m+2)(m+3)$$