How do you simplify the expression 5(2y-5)(2y+5) -4(y-2)(y+3) - (2y+1)^2?

Feb 21, 2017

$12 {y}^{2} - 8 y - 102$

Explanation:

Since

$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

and

$\left(a + b\right) \left(c + d\right) = a c + a d + b c + b d$

and

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

you would expand the expression:

$5 \left(4 {y}^{2} - 25\right) - 4 \left({y}^{2} + 3 y - 2 y - 6\right) - \left(4 {y}^{2} + 4 y + 1\right)$

and multipy:

$20 {y}^{2} - 125 - 4 {y}^{2} - 12 y + 8 y + 24 - 4 {y}^{2} - 4 y - 1$

Then let's sum the like terms:

$12 {y}^{2} - 8 y - 102$