Binomial theorem

(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k}

Result unit: — (expression)

What it describes

Expansion of the n-th power of a binomial using binomial coefficients.

a, b

terms of the binomial

n

exponent

k

summation index

The coefficients in the expansion of

(a+b)^n

are binomial coefficients (Pascal's triangle). Each term has the form

\binom{n}{k}a^{n-k}b^k

Expanding powers of a binomial, finding a specific term of the expansion.

Expand

(a+b)^2

using the binomial theorem.

Substitution

n=2

Result

a^2+2ab+b^2

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