How do you find the product #(5x^2-y^2)^2#?

1 Answer
smendyka
Feb 1, 2017

See the entire solution process below:

Explanation:

First, we can rewrite this expression as:

#(5x^2 - y^2)(5x^2 - y^2)#

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(5x^2) - color(red)(y^2))(color(blue)(5x^2) - color(blue)(y^2))# becomes:

#(color(red)(5x^2) xx color(blue)(5x^2)) - (color(red)(5x^2) xx color(blue)(y^2)) - (color(red)(y^2) xx color(blue)(5x^2)) + (color(red)(y^2) xx color(blue)(y^2))#

#25x^4 - 5x^2y^2 - 5x^2y^2 + y^4#

We can now combine like terms:

#25x^4 + (-5 - 5)x^2y^2 + y^4#

#25x^4 -10x^2y^2 + y^4#

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