Question

How do you multiply `(3n-2)(3n^2-8n-5)`?

Answer 1

`9n^3 - 30n^2 + n + 10`

Explanation:

To multiply the two terms in this expression you must multiply each term within the left parenthesis by each term in the right parenthesis:

`(color(red)(3n - 2))(color(blue)(3n^2 - 8n - 5)) ->`

`(color(red)(3n) * color(blue)(3n^2)) - (color(red)(3n) * color(blue)(8n)) - (color(red)(3n) * color(blue)(5)) - (color(red)(2) * color(blue)(3n^2)) + (color(red)(2) * color(blue)(8n)) + (color(red)(2) * color(blue)(5)) ->`

`9n^3 - 24n^2 - 15n - 6n^2 + 16n + 10`

Now we can group and combine like terms:

`9n^3 - 24n^2 - 6n^2 - 15n + 16n + 10`

`9n^3 - (24 + 6)n^2 + (-15 + 16)n + 10`

`9n^3 - 30n^2 + 1n + 10`

`9n^3 - 30n^2 + n + 10`