Question

How do you find the product `(4y^2-3)(4y^2+7y+2)`?

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)(4y^2) - color(red)(3))(color(blue)(4y^2) + color(blue)(7y) + color(blue)(2))` becomes:

`(color(red)(4y^2) xx color(blue)(4y^2)) + (color(red)(4y^2) xx color(blue)(7y)) + (color(red)(4y^2) xx color(blue)(2)) - (color(red)(3) xx color(blue)(4y^2)) - (color(red)(3) xx color(blue)(7y)) - (color(red)(3) xx color(blue)(2))`

`16y^4 + 28y^3 + 8y^2 - 12y^2 - 21y - 6`

We can now combine like terms:

`16y^4 + 28y^3 + (8 - 12)y^2 - 21y - 6`

`16y^4 + 28y^3 - 4y^2 - 21y - 6`