Binomial theorem

If x and a are real numbers, then for all n Є N

(x+a)ⁿ
= ⁿC₀xⁿa⁰ + ⁿC₁x^n-1a¹ +ⁿC₂x^n-2a² + ...+ⁿC_rx^n-ra^r+ ...+ⁿC_n-1x¹a^n-1+ⁿC_nx⁰aⁿ

(x+a)ⁿ
= (r = 0 to n)Σ ⁿC_rx^n-ra^r