How do you multiply (5x^2-5y)^2?

1 Answer
smendyka
Feb 13, 2017

See the entire solution process below:

Explanation:

This expression can be rewritten as:

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

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

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

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

We can now combine like terms:

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

25x^4 - 50x^2y + 25y^2

If necessary, we can factor out a 25 from each term to give:

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

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