Question

How do you multiply `(x^2 + -4)(x^2 + -4)`?

Answer 1

See the entire solution process below:

Explanation:

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

`(color(red)(x^2) + color(red)(-4))(color(blue)(x^2) + color(blue)(-4)) ->`

`(color(red)(x^2) - color(red)(4))(color(blue)(x^2) - color(blue)(4))` becomes:

`(color(red)(x^2) xx color(blue)(x^2)) - (color(red)(x^2) xx color(blue)(4)) - (color(red)(4) xx color(blue)(x^2)) + (color(red)(4) xx color(blue)(4))`

`x^4 - 4x^2 - 4x^2 + 16`

We can now combine like terms:

`x^4 + (-4 - 4)x^2 + 16`

`x^4 + (-8)x^2 + 16`

`x^4 - 8x^2 + 16`