1.1.4.3 Binomial Theorem | Positive Integral Index | Negative Intetgral Index | Rational Index

In this video, you will get the idea of Binomial Theorem expansion with Positive Integral Index, Negative Intetgral Index and Rational Index.

1 term (monomial) : 16, 4𝑥, 3𝑥^7, 𝑎^4 𝑏
2 terms (binomial) : 𝑥+𝑦, 𝑝−𝑞, 𝑥^2−4𝑦, 7𝑎+3𝑏^2
3 terms (trinomial) : 𝑥+2𝑦−3𝑧, 𝑎−𝑏−𝑐, 2𝑥+3𝑦^4+6𝑧
4 or more terms (multinomial) : 𝑤+𝑥+5𝑦+𝑧, 2𝑎^3−𝑏−𝑐−𝑑^2+3𝑒

Binomial Theorem is a statement that describes this expansion of a binomial.

1. (_^𝑛)𝐶_0 , (_^𝑛)𝐶_1 . (_^𝑛)𝐶_2 ... (_^𝑛)𝐶_𝑛 are known as binomial coefficients.
2. Exponents of 𝑎: exponent of 𝑎 in the term with binomial coefficient (_^𝑛)𝐶_𝑟 will be 𝑛−𝑟.
3. Exponents of 𝑏: exponent of 𝑏 in the term with binomial coefficient (_^𝑛)𝐶_𝑟 will be 𝑟.
4. Sum of the exponents of 𝑎 and 𝑏 in each term: 𝑛
5. Total terms after expansion: 𝑛+1
6. Index: MUST be positive integer. When 𝒏 goes negative OR 𝒏 is rational, then this will not work.

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