Question

How do you multiply `(3sqrt2 - 9)(3sqrt2 +9)`?

Answer 1

This is of the form `(a-b)(a+b) = a^2-b^2`, so

`(3sqrt(2)-9)(3sqrt(2)+9) = (3sqrt(2))^2-9^2 = 18-81 = -63`

Explanation:

Standard difference of squares identity.

`(3sqrt(2)-9)(3sqrt(2)+9)`

`= (3sqrt(2))^2-9^2`

`= (3^2sqrt(2)^2)-9^2`

`=(9*2)-81 = 18-81 = -63`