SOLUTION: Multiply: (5√[3] + √[5])(√[3] – 2√[5])

Algebra ->  Radicals -> SOLUTION: Multiply: (5√[3] + √[5])(√[3] – 2√[5])       Log On


   

Question 167727: Multiply:
(5√[3] + √[5])(√[3] – 2√[5])
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%285%2Asqrt%283%29%2Bsqrt%285%29%29%28sqrt%283%29-2%2Asqrt%285%29%29 Start with the given expression.


Now let's FOIL the expression.


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


Multiply the First terms:%285%2Asqrt%283%29%29%2A%28sqrt%283%29%29=5%2Asqrt%283%2A3%29=5%2A3=15.


Multiply the Outer terms:.


Multiply the Inner terms:%28sqrt%285%29%29%2A%28sqrt%283%29%29=sqrt%283%2A5%29=sqrt%2815%29.


Multiply the Last terms:%28sqrt%285%29%29%2A%28-2%2Asqrt%285%29%29-2%2Asqrt%285%2A5%29=-2%2A5=-10.


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15-10%2Asqrt%2815%29%2Bsqrt%2815%29-10 Now collect every term to make a single expression.


5-9%2Asqrt%2815%29 Now combine like terms.


So %285sqrt%283%29%2Bsqrt%285%29%29%28sqrt%283%29-2sqrt%285%29%29 FOILs to 5-9%2Asqrt%2815%29.


In other words, %285%2Asqrt%283%29%2Bsqrt%285%29%29%28sqrt%283%29-2%2Asqrt%285%29%29=5-9%2Asqrt%2815%29.