# How do you simplify (5x+4)(5x+4)(5x-4)(5x-4)?

Aug 3, 2015

$625 {x}^{4} - 800 {x}^{2} + 256$

#### Explanation:

It's beneficial to rearrange the factors first in this case, and write the whole thing as a square, because when you use the FOIL (First, Outside, Inside, Last) method, the $\setminus \pm$ signs will cause cancellation for the first step after that to make your work a bit easier. Like this:

$\left(5 x + 4\right) \left(5 x + 4\right) \left(5 x - 4\right) \left(5 x - 4\right) = {\left(\left(5 x + 4\right) \left(5 x - 4\right)\right)}^{2}$

$= {\left(25 {x}^{2} - 20 x + 20 x - 16\right)}^{2} = {\left(25 {x}^{2} - 16\right)}^{2}$

Now just FOIL this expression out:

$\left(25 {x}^{2} - 16\right) \left(25 {x}^{2} - 16\right) = 625 {x}^{4} - 800 {x}^{2} + 256$