##### Binomial Theorem – Notes

**Binomial Theorem for Positive Integral Indices**

The number of terms in an expansion is one more than the power of the binomial.

The coefficients of the first and the last terms of an expansion are both 1.

(x + y)^{n} = ^{n}C_{0}x^{n} + ^{n}c_{1}x^{n – 1}y + ^{n}C_{2}x^{n – 2}y^{2} +…. + ^{n}C_{n }– _{1}xy^{n – 1} + ^{n}C_{n}y^{n}

^{n}C_{0}, ^{n}C_{1}, ^{n}C_{2},… ^{n}C_{n – 1}, ^{n}C_{n} are called binomial coefficients.

**General and Middle Terms**

In the expansion (x + y)^{n}

- General term, T
_{r + 1}=^{n}C_{r}x^{n – r}y^{r} - Middle term when n is even = (
^{th}term

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ShikshaHouse

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Class 11th Maths 8 - Binomial Theorem - Notes

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