SOLUTION: Multiply (3x+3y)^2(2x+3y)

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Question 198861: Multiply (3x+3y)^2(2x+3y)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's FOIL %283x%2B3y%29%5E2


%283x%2B3y%29%5E2 Start with the given expression.


%283x%2B3y%29%283x%2B3y%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


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


%28highlight%283x%29%2B3y%29%28highlight%283x%29%2B3y%29 Multiply the First terms:%283%2Ax%29%2A%283%2Ax%29=9%2Ax%5E2.


%28highlight%283x%29%2B3y%29%283x%2Bhighlight%283y%29%29 Multiply the Outer terms:%283%2Ax%29%2A%283%2Ay%29=9%2Ax%2Ay.


%283x%2Bhighlight%283y%29%29%28highlight%283x%29%2B3y%29 Multiply the Inner terms:%283%2Ay%29%2A%283%2Ax%29=9%2Ax%2Ay.


%283x%2Bhighlight%283y%29%29%283x%2Bhighlight%283y%29%29 Multiply the Last terms:%283%2Ay%29%2A%283%2Ay%29=9%2Ay%5E2.


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So we have the terms: 9%2Ax%5E2, 9%2Ax%2Ay, 9%2Ax%2Ay, 9%2Ay%5E2


9%2Ax%5E2%2B9%2Ax%2Ay%2B9%2Ax%2Ay%2B9%2Ay%5E2 Now add every term listed above to make a single expression.


9%2Ax%5E2%2B18%2Ax%2Ay%2B9%2Ay%5E2 Now combine like terms.


So %283x%2B3y%29%5E2 FOILs to 9%2Ax%5E2%2B18%2Ax%2Ay%2B9%2Ay%5E2.


In other words, %283x%2B3y%29%5E2=9%2Ax%5E2%2B18%2Ax%2Ay%2B9%2Ay%5E2.


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So %283x%2B3y%29%5E2%282x%2B3y%29 becomes %289x%5E2%2B18xy%2B9y%5E2%29%282x%2B3y%29



%289x%5E2%2B18xy%2B9y%5E2%29%282x%2B3y%29 Start with the given expression.


%282x%2B3y%29%289x%5E2%2B18xy%2B9y%5E2%29 Rearrange the terms.


2x%289x%5E2%2B18xy%2B9y%5E2%29%2B3y%289x%5E2%2B18xy%2B9y%5E2%29 Expand


Distribute


18x%5E3%2B36x%5E2%2Ay%2B18x%2Ay%5E2%2B27x%5E2%2Ay%2B54x%2Ay%5E2%2B27y%5E3 Multiply


18x%5E3%2B63x%5E2%2Ay%2B72x%2Ay%5E2%2B27y%5E3 Combine like terms.


So %283x%2B3y%29%5E2%2A%282x%2B3y%29=18x%5E3%2B63x%5E2%2Ay%2B72x%2Ay%5E2%2B27y%5E3