Question

How do you find the product of `(3d+3)(2d^2+5d-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)(3d) + color(red)(3))(color(blue)(2d^2) + color(blue)(5d) - color(blue)(2))` becomes:

`(color(red)(3d) xx color(blue)(2d^2)) + (color(red)(3d) xx color(blue)(5d)) - (color(red)(3d) xx color(blue)(2)) + (color(red)(3) xx color(blue)(2d^2)) + (color(red)(3) xx color(blue)(5d)) - (color(red)(3) xx color(blue)(2))`

`6d^3 + 15d^2 - 6d + 6d^2 + 15d - 6`

We can now group and combine like terms:

`6d^3 + 15d^2 + 6d^2 - 6d + 15d - 6`

`6d^3 + (15 + 6)d^2 + (-6 + 15)d - 6`

`6d^3 + 21d^2 + 9d - 6`