# How do you simplify (5y+3)(5y-3)(25y^2+9)?

Jun 22, 2015

$\left(5 y + 3\right) \left(5 y - 3\right) \left(25 {y}^{2} + 9\right) = \left(25 {y}^{2} - 9\right) \left(25 {y}^{2} + 9\right) = 625 {y}^{4} - 81$

#### Explanation:

This uses the difference of squares identity twice:

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

$\left(5 y + 3\right) \left(5 y - 3\right) \left(25 {y}^{2} + 9\right)$

$= \left({\left(5 y\right)}^{2} - {3}^{2}\right) \left(25 {y}^{2} + 9\right)$

$= \left(25 {y}^{2} - 9\right) \left(25 {y}^{2} + 9\right)$

$= \left({\left(25 {y}^{2}\right)}^{2} - {9}^{2}\right)$

$= 625 {y}^{4} - 81$