Question

How do you find the product `(4a+7)(9a^2+2a-7)`?

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)(4a) + color(red)(7))(color(blue)(9a^2) + color(blue)(2a) - color(blue)(7))` becomes:

`(color(red)(4a) xx color(blue)(9a^2)) + (color(red)(4a) xx color(blue)(2a)) - (color(red)(4a) xx color(blue)(7)) + (color(red)(7) xx color(blue)(9a^2)) + (color(red)(7) xx color(blue)(2a)) - (color(red)(7) xx color(blue)(7))`

`36a^3 + 8a^2 - 28a + 63a^2 + 14a - 49`

We can now group and combine like terms:

`36a^3 + 8a^2 + 63a^2 - 28a + 14a - 49`

`36a^3 + (8 + 63)a^2 + (-28 + 14)a - 49`

`36a^3 + 71a^2 + (-14)a - 49`

`36a^3 + 71a^2 - 14a - 49`