SOLUTION: Can you please help me solve this problem? [(2)+(the square root of 7)]times[(2)-(the square root of 7)]

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Question 190606: Can you please help me solve this problem? [(2)+(the square root of 7)]times[(2)-(the square root of 7)]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282%2Bsqrt%287%29%29%282-sqrt%287%29%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%282%29%2Bsqrt%287%29%29%28highlight%282%29-sqrt%287%29%29 Multiply the First terms:%282%29%2A%282%29=4.


%28highlight%282%29%2Bsqrt%287%29%29%282%2Bhighlight%28-sqrt%287%29%29%29 Multiply the Outer terms:%282%29%2A%28-sqrt%287%29%29=-2%2Asqrt%287%29.


%282%2Bhighlight%28sqrt%287%29%29%29%28highlight%282%29-sqrt%287%29%29 Multiply the Inner terms:%28sqrt%287%29%29%2A%282%29=2%2Asqrt%287%29.


%282%2Bhighlight%28sqrt%287%29%29%29%282%2Bhighlight%28-sqrt%287%29%29%29 Multiply the Last terms:%28sqrt%287%29%29%2A%28-sqrt%287%29%29=-sqrt%2849%29=-7.


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So we have the terms: 4, -2%2Asqrt%287%29, 2%2Asqrt%287%29, and -7


4-2%2Asqrt%287%29%2B2%2Asqrt%287%29-7 Now add every term listed above to make a single expression.


-3 Now combine like terms.


So %282%2Bsqrt%287%29%29%282-sqrt%287%29%29 FOILs to -3.


In other words, %282%2Bsqrt%287%29%29%282-sqrt%287%29%29=-3.