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

1 Answer
Aug 3, 2015

Answer:

#625x^4-800x^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 #\pm# signs will cause cancellation for the first step after that to make your work a bit easier. Like this:

#(5x+4)(5x+4)(5x-4)(5x-4)=((5x+4)(5x-4))^2#

#=(25x^2-20x+20x-16)^2=(25x^2-16)^2#

Now just FOIL this expression out:

#(25x^2-16)(25x^2-16)=625x^4-800x^2+256#