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(a+b)n=∑k=0n(nk)an−kbk(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k(a+b)n=∑k=0n(kn)an−kbk
nnn choose k=n!/(k!(n−k)!)k = n! / (k!(n-k)!)k=n!/(k!(n−k)!)
Binomial coefficient, xxx power, and yyy power.
(x+y)2=x2+2xy+y2(x + y)^2 = x^2 + 2xy + y^2(x+y)2=x2+2xy+y2
(x+1)3=x3+3x2+3x+1(x + 1)^3 = x^3 + 3x^2 + 3x + 1(x+1)3=x3+3x2+3x+1
The total number of terms is n+1n + 1n+1.
Each number is the sum of the two above; rows give coefficients.
The term is given by C(n,k)(an−k)(bk)(−1)kC(n, k)(a^{n-k})(b^k)(-1)^kC(n,k)(an−k)(bk)(−1)k.
It provides coefficients for binomial distributions.
444 choose 222 = 666 ways.
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