Question

Simplify (3sqrt.2+2sqrt.3+sqrt.6)(3sqrt.2-2sqrt.3+sqrt.6)

Answer 1

\[(3\sqrt{2}+2\sqrt{3}+\sqrt{6})(3\sqrt{2}-2\sqrt{3}+\sqrt{6})\]

Answer 2

To make it simple, replace these expression by letters
[(a + b) + c][(a -b) + c] = (a^2 - b^2) + c(a + b) + c(a -b) + c^2 =
= (a^2 - b^2) + c(a^2 - b^2) + c^2. (1)
Now, back to the numbers
a = 3V2 -> a^2 = 9*2 = 18
b= 2V3 -> b^2 = 4*3 = 12
c = V6 -> c^2 = 6.
Replace these values into the expression (1):
(18 - 12) + V6(18 - 12) + 6 = 12 + 6*V6 = 6(2 + V6)

Answer 3

Thanks, I think i understand the method you're using, you're treating the expression a+b and a-b as a variable, correct?

Answer 4

Not variable. Solving is based on the popular identity: a^2 - b^2 = (a -b)(a + b). The numbers are grouped in a way to allow applying this identity.