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

1 Answer
smendyka
Mar 17, 2017

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#

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