How do you multiply #(3n-2)(3n^2-8n-5)#?

1 Answer
smendyka
Dec 21, 2016

#9n^3 - 30n^2 + n + 10#

Explanation:

To multiply the two terms in this expression you must multiply each term within the left parenthesis by each term in the right parenthesis:

#(color(red)(3n - 2))(color(blue)(3n^2 - 8n - 5)) ->#

#(color(red)(3n) * color(blue)(3n^2)) - (color(red)(3n) * color(blue)(8n)) - (color(red)(3n) * color(blue)(5)) - (color(red)(2) * color(blue)(3n^2)) + (color(red)(2) * color(blue)(8n)) + (color(red)(2) * color(blue)(5)) ->#

#9n^3 - 24n^2 - 15n - 6n^2 + 16n + 10#

Now we can group and combine like terms:

#9n^3 - 24n^2 - 6n^2 - 15n + 16n + 10#

#9n^3 - (24 + 6)n^2 + (-15 + 16)n + 10#

#9n^3 - 30n^2 + 1n + 10#

#9n^3 - 30n^2 + n + 10#

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