How do you solve (2+sqrt6)(2-sqrt6)?

1 Answer
Apr 25, 2018

(2+sqrt{6})(2-sqrt{6}) = -2

Explanation:

As you can see we have two binomials multiplied by each other of the form (a+b)(a-b).

There is a useful shortcut for this type of expression:
(a+b)(a-b) = a^2 - b^2

In this case a=2 and b=sqrt{6}

So

(2+sqrt{6})(2-sqrt{6}) = 2^2 - sqrt{6}^2

(2+sqrt{6})(2-sqrt{6}) = 4 - 6

(2+sqrt{6})(2-sqrt{6}) = -2