SOLUTION: (1-√5)(1+√5) show work (:

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Question 582737: (1-√5)(1+√5) show work (:
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281-sqrt%285%29%29%281%2Bsqrt%285%29%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%281%29-sqrt%285%29%29%28highlight%281%29%2Bsqrt%285%29%29 Multiply the First terms:%281%29%2A%281%29=1.


%28highlight%281%29-sqrt%285%29%29%281%2Bhighlight%28sqrt%285%29%29%29 Multiply the Outer terms:%281%29%2A%28sqrt%285%29%29=sqrt%285%29.


%281%2Bhighlight%28-sqrt%285%29%29%29%28highlight%281%29%2Bsqrt%285%29%29 Multiply the Inner terms:%28-sqrt%285%29%29%2A%281%29=-sqrt%285%29.


%281%2Bhighlight%28-sqrt%285%29%29%29%281%2Bhighlight%28sqrt%285%29%29%29 Multiply the Last terms:%28-sqrt%285%29%29%2A%28sqrt%285%29%29=-%28sqrt%285%29%29%5E2.


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So we have the terms: 1, sqrt%285%29, -sqrt%285%29, -%28sqrt%285%29%29%5E2


1%2Bsqrt%285%29-sqrt%285%29-%28sqrt%285%29%29%5E2 Now add every term listed above to make a single expression.


1-%28sqrt%285%29%29%5E2 Now combine like terms.


1-5 Square sqrt%285%29 to get 5.


-4 Subtract


So %281-sqrt%285%29%29%281%2Bsqrt%285%29%29 FOILs and simplifies to -4.


In other words, %281-sqrt%285%29%29%281%2Bsqrt%285%29%29=-4.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1-√5)(1+√5)
---
Use FOIL:
F: 1*1 = 1
O:1*sqrt(5)= sqrt(5)
I:1*-sqrt(5) = -sqrt(5)
L:-sqrt(5)*sqrt(5) = -5
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Combine:
1 + sqrt(5)-sqrt(5)-5
-----
= 1-5
= -4
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Cheers,
Stan H.
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