Intermediate Algebra (12th Edition)

$2(7m+3n)^2$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $98m^2+84mn+18n^2 ,$ factor first the $GCF.$ Then, the resulting trinomial is a perfect square trinomial. Use the factoring of perfect square trinomials. $\bf{\text{Solution Details:}}$ Factoring the $GCF= 2 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 2(49m^2+42mn+9n^2) .\end{array} The trinomial above is a perfect square trinomial. Using $a^2\pm2ab+b^2=(a\pm b)^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2(7m+3n)^2 .\end{array}