Question 596807
Simplify the expression {{{(2+sqrt(3))*(2-sqrt(3))}}}.

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.
{{{(2*2)+(2*(-sqrt(3)))+((sqrt(3))*(2))+((sqrt(3))(-sqrt(3)))}}}
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Now, we simplify. 
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{{{4+ (2*sqrt(3))+((-2)*sqrt(3))-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