SOLUTION: Simplify the expression {{{(2+sqrt(3))*(2-sqrt(3))}}}.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify the expression {{{(2+sqrt(3))*(2-sqrt(3))}}}.      Log On


   

Question 596807: Simplify the expression %282%2Bsqrt%283%29%29%2A%282-sqrt%283%29%29.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the expression %282%2Bsqrt%283%29%29%2A%282-sqrt%283%29%29.
Hi, there--
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We use the distributive property (of multiplication over addition) is solve this. You are multiplying two expressions together. Each expression has two terms.
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First, distribute the 2 in the first expression over each term in the second expression. Then multiply the square root of 3 is the first expression by each term in the second expression.
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You will end up with four one-term expressions added together.

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Now, we simplify.
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4%2B+%282%2Asqrt%283%29%29%2B%28%28-2%29%2Asqrt%283%29%29-3
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Notice that a positive square root of 3 times a negative square root of 3 is a negative square root of 9 which is -3.
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Combine terms. Notice that the second and third terms cancel out because they are the same value (two times the square root of 3), but opposite signs.
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4-3
1
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That's it! There are a few complicated algebra moves were. Feel free to email at the address below if you're not quite sure what I did.
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Ms.Figgy
math.in.the.vortex@gmail.com