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

Jun 4, 2017

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

$20 {n}^{4} - 18 {n}^{3} - 60 {n}^{2} + 42 n + 16$

#### 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:

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

Now collect like terms:

$20 {n}^{4} - 18 {n}^{3} - 60 {n}^{2} + 42 n + 16$

That is the solution.