Question

How do you multiply `(3q - 3) ( - q ^ { 2} + 2q + 4)`?

Answer 1

See a 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)(3q) - color(red)(3))(color(blue)(-q^2 + color(blue)(2q) + color(blue)(4)))` becomes:

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

`-3q^3 + 6q^2 + 12q + 3q^2 - 6q - 12`

We can now group and combine like terms:

`-3q^3 + 6q^2 + 3q^2 + 12q - 6q - 12`

`-3q^3 + (6 + 3)q^2 + (12 - 6)q - 12`

`-3q^3 + 9q^2 + 6q - 12`