## Intermediate Algebra (6th Edition)

$(a-5b)(a+3b)$
The two numbers whose product is $ac= 1(-15)=-15$ and whose sum is $b= -2$ are $\{ -5,3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $a^2-2ab-15b^2$, is \begin{array}{l}\require{cancel} a^2-5ab+3ab-15b^2 \\\\= (a^2-5ab)+(3ab-15b^2) \\\\= a(a-5b)+3b(a-5b) \\\\= (a-5b)(a+3b) .\end{array}