SOLUTION: I need to factor this problem. 8x^3y^2 - 18xy^4

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Question 103908: I need to factor this problem.
8x^3y^2 - 18xy^4
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E3y%5E2+-+18xy%5E4 Start with the given expression


2xy%5E2%284x%5E2+-+9y%5E2%29 Factor out the GCF 2xy%5E2


Now lets factor 4x%5E2+-+9y%5E2


Let a=2x and b=3y

Notice we get

4x%5E2+-+9y%5E2=%282x%29%5E2+-+%283y%29%5E2=a%5E2-b%5E2

So let's use the difference of squares to factor (remember the difference of squares formula is a%5E2-b%5E2=%28a%2Bb%29%28a-b%29


%282x%29%5E2+-+%283y%29%5E2=%282x%2B3y%29%282x-3y%29


2xy%5E2%282x%2B3y%29%282x-3y%29 Now replace 4x%5E2+-+9y%5E2 in 2xy%5E2%284x%5E2+-+9y%5E2%29 with %282x%2B3y%29%282x-3y%29


So 8x%5E3y%5E2+-+18xy%5E4 factors to 2xy%5E2%282x%2B3y%29%282x-3y%29

Answer by stanbon(57219) About Me  (Show Source):
You can put this solution on YOUR website!
factor this problem.
8x^3y^2 - 18xy^4
= 2xy^2(4x^2 - 9y^2)
= 2xy^2(2x-3y)(2x+3y)
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Cheers,
Stan H.