Question

How do you multiply `(3u^2 - n)^2`?

Answer 1

To expand `(3u^2-n)^2` you can use the FOIL method. That stands for:

Fist
Outer
Inner
Last

In essence, you just want to multiply all combinations of the two brackets.

Since `(3u^2-n)` is squared, you can rewrite `(3u^2-n)^2=(3u^2-n)* (3u^2-n)`

Now you use the FOIL method to expand. "First" means you multiply the first term of the first bracket by the first term in the second bracket

`3u^2 * 3u^2= 9u^4`

"Outer" means you multiply the first term in the first bracket by the last term in the second bracket- they are the outermost terms

`3u^2*-n= -3n u^2`

"Inner" means you multiply the second term of the first bracket with the first term in the second bracket

`-n*3u^2= -3n u^2`

"Last" means you mutiply the last terms of each bracket

`-n*-n=n^2`

Now you combine everything:

`(3u^2-n)^2=(3u^2-n)* (3u^2-n)=9u^4 - 3n u^2 - 3n u^2+ n^2= 9u^4 - 6n u^2 + n^2`