Chapter 5 - Sections 5.1-5.7 - Integrated Review - Operations on Polynomials and Factoring Strategies - Page 313: 25

$8x^2(2y-1)(4y^2+2y+1)$

Factoring the $GCF= 8x^2 $ results to $ 8x^2(8y^3-1) $. Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of two cubes, then, \begin{array}{l} 8x^2(8y^3-1) \\= 8x^2[(2y)+(-1)][(2y)^2-(2y)(-1)+(-1)^2] \\= 8x^2(2y-1)(4y^2+2y+1) .\end{array}