SOLUTION: binomials 25x^2-81y^2

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Question 87195: binomials
25x^2-81y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
25x%5E2-81y%5E2 Start with the given expression

Let A%5E2=25x%5E2 and B%5E2=81y%5E2. So we get this:

25x%5E2-81y%5E2=A%5E2-B%5E2

Since A%5E2=25x%5E2, A can be solved for:
sqrt%28A%5E2%29=sqrt%2825x%5E2%29 Take the square root of both sides

A=5x

Since B%5E2=81y%5E2, B can be solved for:
sqrt%28B%5E2%29=sqrt%2881y%5E2%29 Take the square root of both sides

B=9y

Since we have a difference of squares, we can factor it like this:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29



Now replace A and B
25x%5E2-81y%5E2=%285x%2B9y%29%285x-9y%29 Plug in A=5x and B=9y

So the expression

25x%5E2-81y%5E2

factors to

%285x%2B9y%29%285x-9y%29

Notice that if you foil the factored expression, you get the original expression. This verifies our answer.