SOLUTION: Simplify: (2x+4y)^2 thanks a lot!

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Question 151462: Simplify:
(2x+4y)^2
thanks a lot!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282x%2B4y%29%5E2 Start with the given expression.


%282x%2B4y%29%282x%2B4y%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%2B4y%29%28highlight%282x%29%2B4y%29 Multiply the First terms:%282%2Ax%29%2A%282%2Ax%29=4%2Ax%5E2.


%28highlight%282x%29%2B4y%29%282x%2Bhighlight%284y%29%29 Multiply the Outer terms:%282%2Ax%29%2A%284%2Ay%29=8%2Ax%2Ay.


%282x%2Bhighlight%284y%29%29%28highlight%282x%29%2B4y%29 Multiply the Inner terms:%284%2Ay%29%2A%282%2Ax%29=8%2Ax%2Ay.


%282x%2Bhighlight%284y%29%29%282x%2Bhighlight%284y%29%29 Multiply the Last terms:%284%2Ay%29%2A%284%2Ay%29=16%2Ay%5E2.


4%2Ax%5E2%2B8%2Ax%2Ay%2B8%2Ax%2Ay%2B16%2Ay%5E2 Now collect every term to make a single expression.


4%2Ax%5E2%2B16%2Ax%2Ay%2B16%2Ay%5E2 Now combine like terms.


So %282x%2B4y%29%5E2 FOILS to 4%2Ax%5E2%2B16%2Ax%2Ay%2B16%2Ay%5E2.


In other words, %282x%2B4y%29%5E2=4%2Ax%5E2%2B16%2Ax%2Ay%2B16%2Ay%5E2.