Question

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

Answer 1

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`