How do you simplify #(7v + 2) ( 6v ^ { 2} - 5v - 1)#?

1 Answer
smendyka
Sep 4, 2017

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)(7v) + color(red)(2))(color(blue)(6v^2) - color(blue)(5v) - color(blue)(1))# becomes:

#(color(red)(7v) xx color(blue)(6v^2)) - (color(red)(7v) xx color(blue)(5v)) - (color(red)(7v) xx color(blue)(1)) + (color(red)(2) xx color(blue)(6v^2)) - (color(red)(2) xx color(blue)(5v)) - (color(red)(2) xx color(blue)(1))#

#42v^3 - 35v^2 - 7v + 12v^2 - 10v - 2#

We can now group and combine like terms:

#42v^3 - 35v^2 + 12v^2 - 7v - 10v - 2#

#42v^3 + (-35 + 12)v^2 + (-7 - 10)v - 2#

#42v^3 + (-23)v^2 + (-17)v - 2#

#42v^3 - 23v^2 - 17v - 2#

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