SOLUTION: factor completely x^2+8x+15 12x^3-3xy^2

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Question 87365: factor completely
x^2+8x+15


12x^3-3xy^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)



12x%5E3-3xy%5E2

3x%284x%5E2-y%5E2%29 Factor out the GCF

Now lets factor 4x%5E2-y%5E2 using the difference of squares

4x%5E2-1y%5E2 Start with the given expression

Let A%5E2=4x%5E2 and B%5E2=1y%5E2. So we get this:

4x%5E2-1y%5E2=A%5E2-B%5E2

Since A%5E2=4x%5E2, A can be solved for:
sqrt%28A%5E2%29=sqrt%284x%5E2%29 Take the square root of both sides

A=2x

Since B%5E2=1y%5E2, B can be solved for:
sqrt%28B%5E2%29=sqrt%281y%5E2%29 Take the square root of both sides

B=1y

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
4x%5E2-1y%5E2=%282x%2B1y%29%282x-1y%29 Plug in A=2x and B=1y

So the expression

4x%5E2-1y%5E2

factors to

%282x%2B1y%29%282x-1y%29

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

So 12x%5E3-3xy%5E2 factors to


3x%282x%2By%29%282x-y%29