For a binomial expansion:
(x+y)^n(x+y)n we have:
((n),(r))x^(n-r)y^r
sum_(r=0)^(n)((n),(r))x^(n-r)y^r
Where:
((n),(r))=color(white)(0)^n C_(r)=(n!)/(r!(n-r)!)
Beginning with r=0
((6),(0))v^6(-u)^0+((6),(1))v^5(-u)^1+((6),(2))v^4(-u)^2
+((6),(3))v^3(-u)^3+((6),(4))v^2(-u)^4+((6),(5))v^1(-u)^5
((6),(6))v^0(-u)^6
Calculating ((n),(r))
(1)v^6(-u)^0+(6)v^5(-u)^1+(15)v^4(-u)^2
+(20)v^3(-u)^3+(15)v^2(-u)^4+(6)v^1(-u)^5
(1)v^0(-u)^6
Expand brackets and simplify:
color(blue)(v^6-6v^5u+15v^4u^2-20v^3u^3+15v^2u^4-6vu^5+u^6)
To make things easier we can use the following:
color(white)(0)^nC_(r)=color(white)(0)^nC_(n-r)
And:
(-u)^n is negative for odd powers and positive for even powers.
