SOLUTION: Simplify: {{{(4sqrt(3)+7)^2016*(4sqrt(3)-7)^2018}}}

Algebra ->  Radicals -> SOLUTION: Simplify: {{{(4sqrt(3)+7)^2016*(4sqrt(3)-7)^2018}}}      Log On


   

Question 1104229: Simplify:
%284sqrt%283%29%2B7%29%5E2016%2A%284sqrt%283%29-7%29%5E2018
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Instead, I will consider


%284sqrt%283%29%2B7%29%5E2016%2A%284sqrt%283%29-7%29%5E2016.


Due to (a+b)*(a-b) = a%5E2-b%5E2%29, it is equal to  %28%284%2Asqrt%283%29%29%5E2+-+7%5E2%29%5E2016 = %2848-49%29%5E2016 = %28-1%29%5E2016 = 1.


Therefore, the given / (the original) expression is simply

%284%2Asqrt%283%29-7%29%5E2 = 48 - 56*sqrt(3) + 49 = 97 - 56*sqrt(3).


Answer.  %284sqrt%283%29%2B7%29%5E2016%2A%284sqrt%283%29-7%29%5E2018 = 97 - 56*sqrt(3).