How do you multiply #(5n^2+3n-8)(4n^2-6n-2)#?

1 Answer
David G.
Jun 4, 2017

Multiply each term in the first bracket by each term in the second, then collect like terms.

#20n^4-18n^3-60n^2+42n+16#

Explanation:

The key is to ensure that each element in the first bracket is multiplied by each element in the second. There are a number of ways to do that, but here is one:

#(5n^2+3n−8)(4n^2−6n−2)#

can be rearranged as follows:

#5n^2(4n^2−6n−2)+3n(4n^2−6n−2)-8(4n^2−6n−2)#

Now we can multiply through:

#20n^4-30n^3-10n^2+12n^3-18n^2-6n-32n^2+48n+16#

Now collect like terms:

#20n^4-18n^3-60n^2+42n+16#

That is the solution.

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