Question

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

Answer 1

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)