SOLUTION: mulitply and simplify (5sqrt7-15sqrt5) (4sqrt7-12 sqrt5)

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Question 211308: mulitply and simplify
(5sqrt7-15sqrt5) (4sqrt7-12 sqrt5)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%285%2Asqrt%287%29-15%2Asqrt%285%29%29%284%2Asqrt%287%29-12%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:


%28highlight%285%2Asqrt%287%29%29-15%2Asqrt%285%29%29%28highlight%284%2Asqrt%287%29%29-12%2Asqrt%285%29%29 Multiply the First terms:%285%2Asqrt%287%29%29%2A%284%2Asqrt%287%29%29=5%2A4%2Asqrt%287%2A7%29=20%2Asqrt%2849%29=20%2A7=140.


%28highlight%285%2Asqrt%287%29%29-15%2Asqrt%285%29%29%284%2Asqrt%287%29%2Bhighlight%28-12%2Asqrt%285%29%29%29 Multiply the Outer terms:%285%2Asqrt%287%29%29%2A%28-12%2Asqrt%285%29%29=-5%2A12%2Asqrt%287%2A5%29=-60%2Asqrt%2835%29.


%285%2Asqrt%287%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%28highlight%284%2Asqrt%287%29%29-12%2Asqrt%285%29%29 Multiply the Inner terms:%28-15%2Asqrt%285%29%29%2A%284%2Asqrt%287%29%29=-15%2A4%2Asqrt%285%2A7%29=-60%2Asqrt%2835%29.


%285%2Asqrt%287%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%284%2Asqrt%287%29%2Bhighlight%28-12%2Asqrt%285%29%29%29 Multiply the Last terms:%28-15%2Asqrt%285%29%29%2A%28-12%2Asqrt%285%29%29=-15%2A%28-12%29%2Asqrt%285%2A5%29=180%2Asqrt%2825%29=180%2A5=900.


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So we have the terms: 140, -60%2Asqrt%2835%29, -60%2Asqrt%2835%29, and 900


140-60%2Asqrt%2835%29-60%2Asqrt%2835%29%2B900 Now add every term listed above to make a single expression.


1040-120%2Asqrt%2835%29 Combine like terms.


So %285%2Asqrt%287%29-15%2Asqrt%285%29%29%284%2Asqrt%287%29-12%2Asqrt%285%29%29 FOILs to 1040-120%2Asqrt%2835%29.


In other words, %285%2Asqrt%287%29-15%2Asqrt%285%29%29%284%2Asqrt%287%29-12%2Asqrt%285%29%29=1040-120%2Asqrt%2835%29.