SOLUTION: Factorize (x-2y)^3 + (x+2y)^3

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Question 167731: Factorize
(x-2y)^3 + (x+2y)^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=x-2y and z=x%2B2y


So the expression %28x-2y%29%5E3+%2B+%28x%2B2y%29%5E3 then becomes w%5E3+%2B+z%5E3 (through a simple substitution)


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w%5E3%2Bz%5E3 Start with the given expression.


%28w%29%5E3%2B%28z%29%5E3 Rewrite w%5E3 as %28w%29%5E3. Rewrite z%5E3 as %28z%29%5E3.


%28w%2Bz%29%28%28w%29%5E2-%28w%29%28z%29%2B%28z%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%28w%2Bz%29%28w%5E2-wz%2Bz%5E2%29 Multiply


Plug in w=x-2y and z=x%2B2y


FOIL


%28x-2y%2Bx%2B2y%29%28x%5E2-4xy%2B4y%5E2-x%5E2%2B4y%5E2%2Bx%5E2%2B4xy%2B4y%5E2%29 Distribute


2x%28x%5E2%2B12y%5E2%29 Combine like terms.



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Answer:

So %28x-2y%29%5E3+%2B+%28x%2B2y%29%5E3 factors to 2x%28x%5E2%2B12y%5E2%29.