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

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