SOLUTION: multiply. (sqrt8+3sqrt10) (sqrt8-3sqrt10) any help would be appreciated.

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Question 257280: multiply.
(sqrt8+3sqrt10) (sqrt8-3sqrt10)
any help would be appreciated.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%288%29%2B3%2Asqrt%2810%29%29%28sqrt%288%29-3%2Asqrt%2810%29%29 Start with the given expression.


Let x=sqrt%288%29 and y=3%2Asqrt%2810%29

%28x%2By%29%28x-y%29 Replace each sqrt%288%29 term with "x" and each 3%2Asqrt%2810%29 term with "y"


Now let's FOIL the expression.


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


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


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


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


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


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So we have the terms: x%5E2, -x%2Ay, x%2Ay, -y%5E2


x%5E2-x%2Ay%2Bx%2Ay-y%5E2 Now add every term listed above to make a single expression.


x%5E2-y%5E2 Now combine like terms.


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


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


Now plug in x=sqrt%288%29 and y=3%2Asqrt%2810%29


8-%283%2Asqrt%2810%29%29%5E2 Square sqrt%288%29 to get 8.


8-90 Square 3%2Asqrt%2810%29 to get %283%2Asqrt%2810%29%29%5E2=9%2A10=90.


-82 Subtract.


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Answer:


So %28sqrt%288%29%2B3%2Asqrt%2810%29%29%28sqrt%288%29-3%2Asqrt%2810%29%29=-82