## Intermediate Algebra (12th Edition)

$(7x+5q)(2x-5q)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $14x^2-25xq-25q^2 ,$ use the factoring of trinomials in the form $ax^2+bx+c.$ $\bf{\text{Solution Details:}}$ In the trinomial expression above, $a= 14 ,b= -25 ,\text{ and } c= -25 .$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac= 14(-25)=-350$ and whose sum is $b$ are $\left\{ 10,-35 \right\}.$ Using these two numbers to decompose the middle term results to \begin{array}{l}\require{cancel} 14x^2+10xq-35xq-25q^2 .\end{array} Using factoring by grouping, the expression above is equivalent to \begin{array}{l}\require{cancel} (14x^2+10xq)-(35xq+25q^2) \\\\= 2x(7x+5q)-5q(7x+5q) \\\\= (7x+5q)(2x-5q) .\end{array}