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

$2a(3a+2b)[9a^2-6ab+4b^2)$
Factoring the $GCF= 2a$, then the given expression, $54a^4+16ab^3$ is equivalent to \begin{array}{l} 2a(27a^3+8b^3) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of $2$ cubes, then the factored form of the expression, $2a(27a^3+8b^3)$ is \begin{array}{l} 2a(3a+2b)[(3a)^2-(3a)(2b)+(2b)^2] \\\\= 2a(3a+2b)[9a^2-6ab+4b^2) .\end{array}