Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1, Exe-2, Exe-3 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

## Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9

Board | ISC |

Class | 11 |

Subject | Mathematics |

Chapter-9 | Binomial Theorem |

Session | 2024-25 |

Topics | Solutions of ML Aggarwal |

**Binomial Theorem**

The binomial theorem states a formula for the expression of the powers of sums

Expand (a + b)^{n} = ^{n}C_{0} a^{n} + ^{n}C_{1} a^{n-1} b + ^{n}C_{2} a^{n-2} b^{2} + … + ^{n}C_{n-1} a b^{n-1} + ^{n}C_{n} b^{n}

#### special cases from the binomial theorem

- (x + y)
^{n}=^{n}C_{0}x^{n}+^{n}C_{1}x^{n-1}by+^{n}C_{2}x^{n-2}y^{2}+ … +^{n}C_{n-1}x y^{n-1}+^{n}C_{n}x^{n} - (x – y)
^{n}=^{n}C_{0}x^{n}–^{n}C_{1}x^{n-1}by +^{n}C_{2}x^{n-2}y^{2}+ … + (-1)^{n}^{n}C_{n}x^{n} - (1 – x)
^{n}=^{n}C_{0}–^{n}C_{1}x +^{n}C_{2}x^{2}– …. (-1)^{n}^{n}C_{n}x^{n} - ,
^{n}C_{0}=^{n}C_{n}= 1

**General and Middle terms**

Consider the binomial expansion, (a + b)^{n} = ^{n}C_{0} a^{n} + ^{n}C_{1} a^{n-1} b + ^{n}C_{2} a^{n-2} b^{2} + … + ^{n}C_{n-1} a b^{n-1} + ^{n}C_{n} b^{n}

Here, First term = ^{n}C_{0} a^{n}

Second term = ^{n}C_{1} a^{n-1} b

Third term = ^{n}C_{2} a^{n-2} b^{2}

Similarly, we can write the (r + 1)th term as:

^{n}C_{r} a^{n-r} b^{r}

This is the general term of the given expansion.

Thus, (r + 1)Th term, i.e. T_{r+1} = ^{n}C_{r} a^{n-r} b^{r} is called the middle term of the expansion (a + b)^{n}.

**Exe-9.1**

Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9

**Exe-9.2**

Binomial Theorem Class-11 Maths

**Exe-9.3**

Ch-9 Binomial Theorem ISC Class-11 Maths

**Chapter Test**

Binomial Theorem ISC Class-11 Maths Solutions Chapter-9

**-: End of Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions :-**

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