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

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Answer 1 · 2015-04-10T10:19:15

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#