GMAT question - Simplify 1/3 -... - Review
Type: Problem Solving
Difficulty: 
Simplify %5E2)
(a+b)%20=%20%20a%5E%7B2%7D%20-%20b%5E%7B2%7D)
%7D%7B(3%20-%20%5Csqrt%7B8%7D)%20%5Ctimes%20(3%20+%20%5Csqrt%7B8%7D)%7D%5Cright)%20%5E%202%0D%0A)
%5E2%0D%0A&=%20%5Cleft(%5Cfrac%7B3%20+%20%5Csqrt%7B8%7D%7D%7B9%20-%208%7D%5Cright)%5E2%20%5C%5C%0D%0A&=%20%5Cleft(%5Cfrac%7B3%20+%20%5Csqrt%7B8%7D%7D%7B1%7D%5Cright)%5E2%20%5C%5C%0D%0A&=%20(3%20+%20%5Csqrt%7B8%7D)%5E2%0D%0A%5Cend%7Bsplit%7D%0D%0A)
%5E2%20%0D%0A&=%20%203%5E2%20+%202(3%20%5Ctimes%20%5Csqrt%7B8%7D)%20+%20(%5Csqrt%7B8%7D)%5E2%20%5C%5C%0D%0A&=%209%20+%206%20%5Csqrt%7B8%7D%20+%208%20%5C%5C%0D%0A&=%2017%20+%206%20%5Csqrt%7B8%7D%0D%0A%5Cend%7Bsplit%7D%0D%0A)
Explanation
This question is a little bit tricky. If you try just multiplying it out you will end up with a sum including square roots at the bottom of the fraction that you can't seem to simplify further.
To be able to answer it you need to know the formula for the difference between two squares.
This formula gives us the trick to get rid of the square roots from the denominator of the fraction.
Multiply the numerator and denominator by
Simplify to give
Multiplying out give us
So the correct answer is E.
I'm doomed!
Where is the "2(3 x sqrt of 8)" come from under the first line of "Multiplying out gives us"??? I get 3 squared and (sqrt of 8) squared but don't understand where this piece in the middle comes from?
Ah maybe it's FOIL! (First Outside Inside Last)? Can someone confirm?
Let me illustrate FOIL with the "equation" they list in the first step; (a - b)(a + b);
First = a x a or a^2
Outside = a x b or ab
Inside = -b x a or -ab
Last = -b x b
So this gives us; a^2 + ab - ab - b^2
Simplify = a^2 - b^2