## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-(xy+2)(xy+6)$
The given expression, $-12-x^2y^2-8xy ,$ can be re-written as \begin{array}{l} -x^2y^2-8xy-12 \\\\= -(x^2y^2+8xy+12) .\end{array} The two numbers whose product is $ac= 1(12)=12$ and whose sum is $b= 8$ are $\{ 2,6 \}$. Using these two numbers to decompose the middle term of the expression, $-(x^2y^2+8xy+12) ,$ then the factored form is \begin{array}{l} -(x^2y^2+2xy+6xy+12) \\\\= -[(x^2y^2+2xy)+(6xy+12)] \\\\= -[xy(xy+2)+6(xy+2)] \\\\= -[(xy+2)(xy+6)] \\\\= -(xy+2)(xy+6) .\end{array}