Question

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

Answer 1

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.