Chapter 5 - Section 5.6 - A General Factoring Strategy - Exercise Set - Page 379: 51

$2(4y+1)(2y-1)$

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-^2$. The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$. The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$. Hence here: $16y^2-4y-2=\\=16y^2+4y-8y-2\\=4y(4y+1)-2(4y+1)\\=(4y+1)(4y-2)\\=(4y+1)2(2y-1)\\=2(4y+1)(2y-1)$