SOLUTION: (2x+9y)^2

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Question 788451: (2x+9y)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


%282x%2B9y%29%282x%2B9y%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%282x%29%2B9y%29%28highlight%282x%29%2B9y%29 Multiply the First terms:%282%2Ax%29%2A%282%2Ax%29=4%2Ax%5E2.


%28highlight%282x%29%2B9y%29%282x%2Bhighlight%289y%29%29 Multiply the Outer terms:%282%2Ax%29%2A%289%2Ay%29=18%2Ay%2Ax.


%282x%2Bhighlight%289y%29%29%28highlight%282x%29%2B9y%29 Multiply the Inner terms:%289%2Ay%29%2A%282%2Ax%29=18%2Ay%2Ax.


%282x%2Bhighlight%289y%29%29%282x%2Bhighlight%289y%29%29 Multiply the Last terms:%289%2Ay%29%2A%289%2Ay%29=81%2Ay%5E2.


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So we have the terms: 4%2Ax%5E2, 18%2Ay%2Ax, 18%2Ay%2Ax, 81%2Ay%5E2


4%2Ax%5E2%2B18%2Ay%2Ax%2B18%2Ay%2Ax%2B81%2Ay%5E2 Now add every term listed above to make a single expression.


4x%5E2%2B36yx%2B81y%5E2 Now combine like terms.


So %282x%2B9y%29%5E2 FOILs to 4x%5E2%2B36yx%2B81y%5E2.


In other words, %282x%2B9y%29%5E2=4x%5E2%2B36yx%2B81y%5E2.