SOLUTION: Multiply: (8√[6] + 3√[2])(4√[6] – 5√[2])

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Question 147680: Multiply:
(8√[6] + 3√[2])(4√[6] – 5√[2])

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%288%2Asqrt%286%29%2B3%2Asqrt%282%29%29%2A%284%2Asqrt%286%29-5%2Asqrt%282%29%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%288%2Asqrt%286%29%29%2B3%2Asqrt%282%29%29%28highlight%284%2Asqrt%286%29%29-5%2Asqrt%282%29%29 Multiply the First terms:%288%2Asqrt%286%29%29%2A%284%2Asqrt%286%29%29=%288%2A4%29%2Asqrt%286%2A6%29=32%2A6=192.


%28highlight%288%2Asqrt%286%29%29%2B3%2Asqrt%282%29%29%284%2Asqrt%286%29%2Bhighlight%28-5%2Asqrt%282%29%29%29 Multiply the Outer terms:%288%2Asqrt%286%29%29%2A%28-5%2Asqrt%282%29%29=%288%2A-5%29%2Asqrt%286%2A2%29=-40%2A2%2Asqrt%283%29=-80%2Asqrt%283%29.


%288%2Asqrt%286%29%2Bhighlight%283%2Asqrt%282%29%29%29%28highlight%284%2Asqrt%286%29%29-5%2Asqrt%282%29%29 Multiply the Inner terms:%283%2Asqrt%282%29%29%2A%284%2Asqrt%286%29%29=%283%2A4%29%2Asqrt%282%2A6%29=12%2A2%2Asqrt%283%29=24%2Asqrt%283%29.


%288%2Asqrt%286%29%2Bhighlight%283%2Asqrt%282%29%29%29%284%2Asqrt%286%29%2Bhighlight%28-5%2Asqrt%282%29%29%29 Multiply the Last terms:%283%2Asqrt%282%29%29%2A%28-5%2Asqrt%282%29%29=%283%2A-5%29%2Asqrt%282%2A2%29=-15%2A2=-30.


192-80%2Asqrt%283%29%2B24%2Asqrt%283%29-30 Now collect every term to make a single expression.


162-56%2Asqrt%283%29 Now combine like terms.


So %288%2Asqrt%286%29%2B3%2Asqrt%282%29%29%2A%284%2Asqrt%286%29-5%2Asqrt%282%29%29 FOILS to 162-56%2Asqrt%283%29.


In other words, %288%2Asqrt%286%29%2B3%2Asqrt%282%29%29%2A%284%2Asqrt%286%29-5%2Asqrt%282%29%29=162-56%2Asqrt%283%29.