Answer
$(a+b-5)(a+b+2)$
Work Step by Step
If we let $u=a+b$, the given expression becomes:
$=u^2-3u-10$
RECALL:
A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$.
The trinomial's factored form will be:
$x^2+bx+c=(x+d)(x+e)$
The trinomial in the expression above has $a=1, b=-3$, and $c=-10$.
Note that $-10=-5(2)$ and $-3 = -5+2$.
This means that $d=-5$ and $e=2$
Thus, the factored form of the trinomial is:
$=[u+(-5)][u+2] = (u-5)(u+2)$
Replace $u$ with its equivalent $a+b$ to otain:
$=[(a+b)-5][(a+b+2]
\\=(a+b-5)(a+b+2)$