SOLUTION: Can you please explain how to solve for special polynomial products to the third degree. (x+y) to the third power. I know the answer is x to the third+3x squared y + 3xy squared+

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please explain how to solve for special polynomial products to the third degree. (x+y) to the third power. I know the answer is x to the third+3x squared y + 3xy squared+      Log On


   

Question 182046: Can you please explain how to solve for special polynomial products to the third degree. (x+y) to the third power. I know the answer is x to the third+3x squared y + 3xy squared+y squared. I need help understanding how to get this answer.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2By%29%5E3 Start with the given expression.


%28x%2By%29%28x%2By%29%28x%2By%29 Expand. Remember something like A%5E3 expands to A%5E3=A%2AA%2AA


Now let's FOIL the first two "x+y" terms:

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%28x%2By%29%28x%2By%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28x%29%2By%29%28highlight%28x%29%2By%29 Multiply the First terms:%28x%29%2A%28x%29=x%5E2.


%28highlight%28x%29%2By%29%28x%2Bhighlight%28y%29%29 Multiply the Outer terms:%28x%29%2A%28y%29=x%2Ay.


%28x%2Bhighlight%28y%29%29%28highlight%28x%29%2By%29 Multiply the Inner terms:%28y%29%2A%28x%29=x%2Ay.


%28x%2Bhighlight%28y%29%29%28x%2Bhighlight%28y%29%29 Multiply the Last terms:%28y%29%2A%28y%29=y%5E2.


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x%5E2%2Bxy%2Bxy%2By%5E2 Now collect every term to make a single expression.


x%5E2%2B2xy%2By%5E2 Now combine like terms.


So %28x%2By%29%28x%2By%29 FOILs to x%5E2%2B2xy%2By%5E2.


In other words, %28x%2By%29%28x%2By%29=x%5E2%2B2xy%2By%5E2.


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So this means that %28x%2By%29%28x%2By%29%28x%2By%29 then becomes %28x%5E2%2B2xy%2By%5E2%29%28x%2By%29


%28x%2By%29%28x%5E2%2B2xy%2By%5E2%29 Rearrange the terms.


x%28x%5E2%2B2xy%2By%5E2%29%2By%28x%5E2%2B2xy%2By%5E2%29 Expand. Note: %28A%2BB%29%28C%2BD%2BE%29=A%28C%2BD%2BE%29%2BB%28C%2BD%2BE%29


Distribute.


x%5E3%2B2x%5E2%2Ay%2Bxy%5E2%2Bx%5E2%2Ay%2B2xy%5E2%2By%5E3 Multiply.


x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3 Now combine like terms.


So %28x%2By%29%28x%5E2%2B2xy%2By%5E2%29 expands to x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3.


In other words, %28x%2By%29%28x%5E2%2B2xy%2By%5E2%29=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3.


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Answer:


So %28x%2By%29%5E3=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3