Intermediate Algebra (6th Edition)

$(2y+3x)(8y-9x)$
The two numbers whose product is $ac= 3(-27)=-432$ and whose sum is $b= 6$ are $\{ 24,-18 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $16y^2+6yx-27x^2$, is \begin{array}{l}\require{cancel} 16y^2+24yx-18yx-27x^2 \\\\= (16y^2+24yx)-(18yx+27x^2) \\\\= 8y(2y+3x)-9x(2y+3x) \\\\= (2y+3x)(8y-9x) .\end{array}