Chapter R - Algebra Reference - R.2 Factoring - R.2 Exercises - Page R-8: 32

$(2a-3b)(2a+3b)(4a^2+9b^2)$

RECALL: $x^2-y^2=(x-y)(x+y)$ The given expression can be written as: $(4a)^2-(9b^2)^2$ Factor this expression using the formula above with $x=4a^2$ and $y=9b^2$ to have: $=(4a^2-9b^2)(4a^2+9b^2) \\=[(2a)^2-(3b)^2](4a^2+9b^2)$ Factor the first binomial using the same formula with $x=2a$ and $y=3b$ to have: $=(2a-3b)(2a+3b)(4a^2+9b^2)$