The math behind poisson and binomial formulas

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The math behind poisson and binomial formulas

In: Mathematics
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The binomial formulas are all based on simple multiplication:

`(a+b)^2 = (a+b)*(a+b) = a*a + a*b + b*a + b*b = a^2 +2ab + b^2`

Binomial theorem defines how a binomial like (1+x), which is the standard form of the binomial, will produce results when it is multiplied or divided in different cases. If (1+x)^n is a binomial, then according to the theorem, its result will be = 1+n*x + n*(n-1)/2!*x^2 + n*(n-1)(n-2)/3!*x^3…x^n. This result is interesting as it produces (a+b)^3= a^3+3ba^2+3ab^2+b^3. See how the exponential value of a decreases from a^3 to a=1 ? and how the value of b increases from b=1 to b^3 ? This is the result of the binomial theorem. Also, due the value of n, we get coefficients of a^2b and ab^2 as three. This the how the binomial will converge, or add up the value of (1+x)^n.