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

$a^3(a-5b)(a+b)$
Factoring the $GCF= a^3$, then the given expression, $a^5-4a^4b-5a^3b^2$ is equivalent to \begin{array}{l} a^3(a^2-4ab-5b^2) .\end{array} The two numbers whose product is $ac= 1(-5)=-5$ and whose sum is $b= -4$ are $\{ -5,1 \}$. Using these two numbers to decompose the middle term of the expression, $a^3(a^2-4ab-5b^2) ,$ then the factored form is \begin{array}{l} a^3(a^2-5ab+ab-5b^2) \\\\= a^3[(a^2-5ab)+(ab-5b^2)] \\\\= a^3[a(a-5b)+b(a-5b)] \\\\= a^3[(a-5b)(a+b)] \\\\= a^3(a-5b)(a+b) .\end{array}