SOLUTION: Multiply, then simplify the product. (3+square root2) to the power of 2

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Question 171553: Multiply, then simplify the product.
(3+square root2) to the power of 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283%2Bsqrt%282%29%29%5E2 Start with the given expression.


%283%2Bsqrt%282%29%29%283%2Bsqrt%282%29%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%283%29%2Bsqrt%282%29%29%28highlight%283%29%2Bsqrt%282%29%29 Multiply the First terms:%283%29%2A%283%29=9.


%28highlight%283%29%2Bsqrt%282%29%29%283%2Bhighlight%28sqrt%282%29%29%29 Multiply the Outer terms:%283%29%2A%28sqrt%282%29%29=3%2Asqrt%282%29.


%283%2Bhighlight%28sqrt%282%29%29%29%28highlight%283%29%2Bsqrt%282%29%29 Multiply the Inner terms:%28sqrt%282%29%29%2A%283%29=3%2Asqrt%282%29.


%283%2Bhighlight%28sqrt%282%29%29%29%283%2Bhighlight%28sqrt%282%29%29%29 Multiply the Last terms:%28sqrt%282%29%29%2A%28sqrt%282%29%29=2.


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9%2B3%2Asqrt%282%29%2B3%2Asqrt%282%29%2B2 Now collect every term to make a single expression.


11%2B6%2Asqrt%282%29 Now combine like terms.


So %283%2Bsqrt%282%29%29%5E2 FOILs to 11%2B6%2Asqrt%282%29.


In other words, %283%2Bsqrt%282%29%29%5E2=11%2B6%2Asqrt%282%29.