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The binomial theorem is pretty interesting.

The statement is as follows:

Given the definition of (nCk), the following is true:

(x+y)^n =

(nC0) x^n + (nC1) x^(n-1)y + (nC2) x^(n-2) y^2 + ... (nCn-1)x y^(n-1) + (nCn) y^n

You can write this using Σ notation:

(x+y)^n = Σ (nCk) x^(n-k) y^k

where 0≤k≤n.

Binomial theorem is a formula for funding any power of a binomial without multiplying at length