Question

How do you find the product of `(-y-3x)(-y+3x)`?

Answer 1

See the entire solution process below:

Explanation:

Solution 1) We can use this formula:

`(a + b)(a - b) = a^2 - b^2`

Substituting `-y` for `a` and `3x` for `b` gives:

`(-y + 3x)(-y - 3x) = (-y)^2 - (3x)^2 = y^2 - 9x^2`

Solution 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)(-y) - color(red)(3x))(color(blue)(-y) + color(blue)(3x))` becomes:

`(color(red)(-y) xx color(blue)(-y)) + (color(red)(-y) xx color(blue)(3x)) - (color(red)(3x) xx color(blue)(-y)) - (color(red)(3x) xx color(blue)(3x))`

`(-y)^2 - 3xy + 3xy - 9x^2`

We can now combine like terms:

`y^2 + (-3 + 3)xy - 9x^2`

`y^2 + 0xy - 9x^2`

`y^2 - 9x^2`