Complete the calculations algebraically

Complete the calculations algebraically?
Find an expression for the mean and stardard deviation for the follow data. Complete the calculations algebraically.
4a+6b , a-b , a+b , 2a-2b

Given 4a + 6b, a - b, a + b, and 2a - 2b, the mean is simply the average:

Mean = [(4a + 6b) + (a - b) + (a + b) + (2a - 2b)]/4

Group terms:

Mean = (4a + a + a + 2a + 6b - b + b - 2b)/4 = (8a + 4b)/4 = 2a + b <== SOLUTION

Given a sample size, n = 4, the standard deviation is given by:

s = √{[1/(n - 1)]Σ(x - Mean)²}

First, let's calculate Σ(x - Mean)².

For the first value, 4a + 6b:

[(4a + 6b) - (2a + b)]² = (4a + 6b - 2a - b)² = (2a + 5b)² = 4a² + 20ab + 25b²

For the second value, a - b:

[(a - b) - (2a + b)]² = (a - b - 2a - b)² = (-a - 2b)² = a² + 4ab + 4b²

For the third value, a + b:

[(a + b) - (2a + b)]² = (a + b - 2a - b)² = (-a)² = a²

For the fourth value, 2a - 2b:

[(2a - 2b) - (2a + b)]² = (2a - 2b - 2a - b)² = (-3b)² = 9b²

Now sum all four results:

Σ(x - Mean)² = (4a² + 20ab + 25b²) + (a² + 4ab + 4b²) + (a²) + (9b²) = 6a² + 24ab + 38b²

Thus, knowing n = 4, the standard deviation is:

s = √{(1/3)](6a² + 24ab + 38b²)} = √{2a² + 8ab + (38/3)b²} <== SOLUTION

(I don't know how to reduce this any further.)