Binomial theorem, also known as Binomial expansion is an outcome of expanding the powers or exponents of binomial or addition of two terms. In Binomial expansion, the coefficient of terms is known as Binomial coefficients . The binomial theorem and its related concepts are used to prove results and solve problems like algebra, calculus, and several other topics of Mathematics.

## Binomial Theorem Statement

Let us consider (n) as a positive integer and the variables ‘a and a’ as real numbers, or complex numbers, or polynomials.

In the expansion of (a + b)ⁿ, the coefficient ak bn-k in the kth term is equivalent to , where

= n!(n – k!)k!

(a + b)ⁿ = k = 0n a™⁻

# Binomial Theorem Special Case

Binomial theorem special cases which are common and familiar to the students of basic algebra includes the following:

(m + n)1 | m + n |

(m + n)2 | m2 + n2 + 2mn |

(m + n)3 | m3 + 3m2n + 3mn2 + n3 |

(m + n)4 | m4 + 4mn3 + 6m2n2 + 4mn + n4 |

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