## College Algebra 7th Edition

$(x+y-6)(x+y-1)$
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: $=[(x+y)-6][(x+y-1] \\=(x+y-6)(x+y-1)$