Question

can someone tell me how to expand the bionomial (d-2)^6?

Answer 1

(d-2)^6
is the same as (d-2)*(d-2)*.... six times.
You can expand it by multiplication, or you can use the binomial expansion formula, where

(a+b)^n
=a^n + na^(n-1)b + n(n-1)/2!a^(n-2)b^2 +
+ ...b^n

where the general term i is
n(n-1)(n-2)..(n-i)/i! * a^(n-i)b^i

Expanding along these lines, we get for
n=1, (a+b)^1 = a+b
n=2, (a+b)^2 = a^2+2ab+b^2
n=3, (a+b)^3 = a^3+3a^2b+3ab^2+b^3
...
with the coefficients being
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 21 15 6 1
....
Each coefficient is the sum of the one immediately above plus the one to the left.
This pattern is called the pascal's triangle.

For more reading, see:
http://en.wikipedia.org/wiki/Binomial_theorem