SOLUTION: please show me how to do this. Multiply: (5√[2] + 3)(√[2] – 2√[3])

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Question 112204: please show me how to do this.
Multiply:
(5√[2] + 3)(√[2] – 2√[3])

Answer by jim_thompson5910(28598) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2Asqrt%282%29%2B3%29%28sqrt%282%29-2%2Asqrt%283%29%29 Start with the given expression


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


Multiply the First terms:%285%2Asqrt%282%29%29%2A%28sqrt%282%29%29=5%2Asqrt%282%2A2%29=5%2A2=10


Multiply the Outer terms:%285%2Asqrt%282%29%29%2A%28-2%2Asqrt%283%29%29=-10%2Asqrt%282%2A3%29=-10%2Asqrt%286%29


Multiply the Inner terms:%283%29%2A%28sqrt%282%29%29=3%2Asqrt%282%29


Multiply the Last terms:%283%29%2A%28-2%2Asqrt%283%29%29=-6%2Asqrt%283%29


10-10%2Asqrt%286%29%2B3%2Asqrt%282%29-6%2Asqrt%283%29 Now collect every term to make a single expression



3%2Asqrt%282%29-6%2Asqrt%283%29-10%2Asqrt%286%29%2B10 Sort the terms


So %285%2Asqrt%282%29%2B3%29%28sqrt%282%29-2%2Asqrt%283%29%29 foils to 3%2Asqrt%282%29-6%2Asqrt%283%29-10%2Asqrt%286%29%2B10