# Binomial Theorem ISC Class-11 Maths ML Aggarwal

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 = nC0 an + nC1 an-1 b + nC2 an-2 b2 + … + nCn-1 a bn-1 + nCn bn

#### special cases from the binomial theorem

• (x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn xn
• (x – y)n = nC0 xn – nC1 xn-1 by + nC2 xn-2 y2 + … + (-1)n nCn xn
• (1 – x)n = nC0 – nC1 x + nC2 x2 – …. (-1)n nCn xn
• , nC0 = nCn = 1

#### General and Middle terms

Consider the binomial expansion, (a + b)n = nC0 an + nC1 an-1 b + nC2 an-2 b2 + … + nCn-1 a bn-1 + nCn bn

Here,  First term = nC0 an

Second term = nC1 an-1 b

Third term = nC2 an-2 b2

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

nCr an-r br

This is the general term of the given expansion.

Thus, (r + 1)Th term, i.e. Tr+1 = nCr an-r br 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

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