Question

How do you multiply `(5k-5)(k^2-4k-5)`?

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)(5k) - color(red)(5))(color(blue)(k^2) - color(blue)(4k) - color(blue)(5))` becomes:

`(color(red)(5k) xx color(blue)(k^2)) - (color(red)(5k) xx color(blue)(4k)) - (color(red)(5k) xx color(blue)(5)) - (color(red)(5) xx color(blue)(k^2)) + (color(red)(5) xx color(blue)(4k)) + (color(red)(5) xx color(blue)(5))`

`5k^3 - 20k^2 -25k - 5k^2 + 20k + 25`

We can now group and combine like terms:

`5k^3 - 20k^2 - 5k^2 -25k + 20k + 25`

`5k^3 + (-20 - 5)k^2 + (-25 + 20)k + 25`

`5k^3 + (-25)k^2 + (-5)k + 25`

`5k^3 - 25k^2 - 5k + 25`

Answer 2

`color(green)(5k^3-25k^2-5k+25`

Explanation:

`color(white)(aaaaaaaaaaaaa)` `k^2-4k-5`
`color(white)(aaaaaaaaaaa)` `xx underline(5k-5)`
`color(white)(aaaaaaaaaaaaa)` `5k^3-20k^2-25k`
`color(white)(aaaaaaaaaaaaaaaaa)` `-5k^2+20k+25`
`color(white)(aaaaaaaaaaaaa)` `overline(5k^3-25k^2-5k+25)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(5k^3-25k^2-5k+25`