How do you simplify (9 + 2sqrt3)(9 - 2sqrt3)(9+23)(923)?

2 Answers
Apr 6, 2018

You can use the identity (a-b)(a+b)=a^2-b^2(ab)(a+b)=a2b2. 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.

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.