Answer
$(x+y-6)(x+y-1)$
Work Step by Step
If we let $u=x+y$, the given expression becomes:
$=u^2-7u+6$
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 $a=1, b=-7$, and $c=6$.
Note that $6=-6(-1)$ and $-7 = -6+(-1)$.
This means that $d=-6$ and $e=-1$
Thus, the factored form of the trinomial is:
$[u+(-6)][u(-1] = (u-)(u-1)$
Replace $u$ with its equivalent $x+y$ to otain:
$=[(x+y)-6][(x+y-1]
\\=(x+y-6)(x+y-1)$
