This is very impressive. Binomial Expansion makes expansion of high power very easy either by using Combinatorial coefficients which you have explained here or using Pascal Triangle. From your work, we can deduce a very simple formula and approach in solving any expansion related to greater powers more than 2.

(a+b)^n=a^n +na^(n-1)b/1! +n(n-1)a^(n-2)b²/2! +n(n-1)(n-2)a^(n-3)b³/3! +. . . . .

Thanks for sharing 💗