(2/3-5/12)^2+(-5/6-2/3)^2

2/3 - 5/12 = 8/12 - 5/12 = 3/12 = 1/4

-5/6 - 2/3 = -5/6 - 4/6 = -9/6 = -3/2

(1/4)^2 + (-3/2)^2 = 1/16 + 9/4 = 1/16 + 36/16 = 37/16

To calculate the expression (2/3 - 5/12)^2 + (-5/6 - 2/3)^2, we need to follow a few steps:

1. Simplify the expressions within the parentheses.
- (2/3 - 5/12) = (8/12 - 5/12) = 3/12 = 1/4
- (-5/6 - 2/3) = (-10/12 - 8/12) = -18/12 = -3/2

2. Square each simplified expression.
- (1/4)^2 = 1/4 * 1/4 = 1/16
- (-3/2)^2 = (-3/2) * (-3/2) = 9/4

3. Add the squared results.
- 1/16 + 9/4 = (1/16)*1 + (9/4)*4 / 16 = 1/16 + 36/16 = 37/16

So, (2/3 - 5/12)^2 + (-5/6 - 2/3)^2 equals 37/16.