I realise you think you know how to do this particular question now. However, recognising a difference of two squares should have been the prefered method of solution right from the get-go in my opinion.
$\displaystyle A^2 - B^2 = (A - B)(A + B)$ and in your case A = m + 1 and B = 3.
Expanding and factorising takes a lot more time, requires more skill and introduces far greater opportunity for error.
Right. Here $\displaystyle (m+1)^2$ is 'a' and 9 is 'b'. So put that in identity $\displaystyle a^2-b^2=(a+b)(a-b)$. what you will get is:
$\displaystyle (m+1)^2-(3)^2$
$\displaystyle =[(m+1)+3][(m+1)-3]$
$\displaystyle =(m+4)(m-2)$
this is your solution.