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

$-2a^4(a-2)^2$
Factoring the negative $GCF= -2a^4$, then the given expression, $-2a^6+8a^5-8a^4$ is equivalent to \begin{array}{l} -2a^4(a^2-4a+4) .\end{array} The trinomial above is a perfect square trinomial since the first and third terms are both perfect squares and the middle term is twice the product of the square roots of the first and third terms. Hence, then the complete factored form is \begin{array}{l} -2a^4(a-2)^2 .\end{array}