How do you simplify #(9 + 2sqrt3)(9 - 2sqrt3)#?

2 Answers
Apr 6, 2018

You can use the identity #(a-b)(a+b)=a^2-b^2#. A quick proof of this:

#(a-b)(a+b)=aa+\cancel{+ab-ba}-b\b=a^2-b^2#

In your specific case, #(9+2\sqrt{3})(9-2\sqrt{3})=9^2-(2\sqrt{3})^2=81-12=69#.

Answer:

#69#

Explanation:

We will use this formula: #(a+b)(a-b)=a^2-b^2#.
Let,
#a=9#
#b=2sqrt3#

Now put these values in the formula:
#(9 + 2sqrt3)(9-2sqrt3)#

#9^2 - (2sqrt3)^2#

#81 - 4*3#

#81 - 12#

and you get #69#.