Question

How do you multiply `(p^4+3p^2-8)(p+1)`?

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)(p^4) + color(red)(3p^2) - color(red)(8))(color(blue)(p) + color(blue)(1))` becomes:

`(color(red)(p^4) xx color(blue)(p)) + (color(red)(p^4) xx color(blue)(1)) + (color(red)(3p^2) xx color(blue)(p)) + (color(red)(3p^2) xx color(blue)(1)) - (color(red)(8) xx color(blue)(p)) - (color(red)(8) xx color(blue)(1))`

`p^5 + p^4 + 3p^3 + 3p^2 - 8p - 8`

Answer 2

`color(green)(p^5+p^4+3p^3+3p^2-8p-8`

Explanation:

`(p^4+3p^2-8)(p+1)`

`color(white)(aaaaaaaaaaaaa)` `p^4+3p^2-8`
`color(white)(aaaaaaaaaaa)` `xx underline(p+1)`
`color(white)(aaaaaaaaaaaaa)` `p^5+3p^3-8p`
`color(white)(aaaaaaaaaaaaaaa)` `p^4+3p^2-8`
`color(white)(aaaaaaaaaaaaa)` `overline(p^5+p^4+3p^3+3p^2-8p-8)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(p^5+p^4+3p^3+3p^2-8p-8)`