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

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Answer 1 · 2018-04-25T21:06:24

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

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#