## Intermediate Algebra (12th Edition)

$(2-x)(2-y)$
$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $4+xy-2y-2x ,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Grouping the first and fourth terms and the second and third terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (4-2x)+(xy-2y) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2(2-x)+y(x-2) \\\\= 2(2-x)-y(2-x) .\end{array} Factoring the $GCF= (2-x)$ of the entire expression above results to \begin{array}{l}\require{cancel} (2-x)(2-y) .\end{array}