Question

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

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

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

`32v^3 - 12v^2 - 16v + 64v^2 - 24v - 32`

We can now group and then combine like terms:

`32v^3 + 64v^2 - 12v^2 - 16v - 24v - 32`

`32v^3 + (64 - 12)v^2 + (-16 - 24)v - 32`

`32v^3 + 52v^2 + (-40)v - 32`

`32v^3 + 52v^2 - 40v - 32`