# Binomial Theorem Notes, Class 11 Mathematics | SwaVid

Binomial Theorem, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/binomial-theorem

Source: https://www.swavid.com/cbse/class-11/maths/chapter/binomial-theorem

# Binomial Theorem

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Mathematics on SwaVid

### Need for binomial theorem

### Pascal's triangle

### Binomial theorem for positive integers

### Special expansions

### Next chapter

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### All chapters

SwaVid › CBSE › Class 11 › Mathematics › Binomial Theorem

Notes written by SwaVid from the NCERT textbook.

Class 11 Mathematics, Chapter 7. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter introduces an algebraic formula to expand any positive integral power of a binomial expression. It provides a systematic method using combinations to write out expansions without repetitive multiplication.

Source: NCERT Mathematics (Reprint 2026-27) , Chapter 7, Binomial Theorem

Multiplying a binomial like (a + b) by itself becomes difficult and lengthy for higher powers. The binomial theorem gives an expansion formula for (a + b)ⁿ directly for any positive integer n.

Pascal's triangle is a triangular arrangement of numbers where each row lists the binomial coefficients for consecutive values of the index n. Each entry inside a row equals the sum of the two numbers directly above it.

The expansion of (a + b)ⁿ has n + 1 terms. The powers of a decrease from n to 0, while the powers of b increase from 0 to n, with coefficients given by ⁿCᵣ.

Replacing b with -b gives the alternating signs expansion of (a - b)ⁿ. Putting a = 1 and b = x gives the standard expansion of (1 + x)ⁿ, which is useful for comparing numbers and approximations.

Try each question first. Then tap it to see the answer.

(x + 2)⁴ = ⁴C₀ x⁴ + ⁴C₁ x³(2) + ⁴C₂ x²(2²) + ⁴C₃ x(2³) + ⁴C₄ (2⁴)

Evaluate combinations: ⁴C₀ = 1, ⁴C₁ = 4, ⁴C₂ = 6, ⁴C₃ = 4, ⁴C₄ = 1

Substitute powers of 2: 1(x⁴) + 4(2x³) + 6(4x²) + 4(8x) + 1(16)

Simplify coefficients: x⁴ + 8x³ + 24x² + 32x + 16

x⁴ + 8x³ + 24x² + 32x + 16

Write 101 as (100 + 1)

(100 + 1)⁴ = ⁴C₀ (100)⁴ + ⁴C₁ (100)³ + ⁴C₂ (100)² + ⁴C₃ (100) + ⁴C₄ (1)

= 1(100000000) + 4(1000000) + 6(10000) + 4(100) + 1(1)

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401

104060401

Write 1.1 as 1 + 0.1

(1 + 0.1)¹⁰⁰⁰⁰ = ¹⁰⁰⁰⁰C₀ + ¹⁰⁰⁰⁰C₁ (0.1) + other positive terms

= 1 + 10000 × 0.1 + other positive terms

= 1 + 1000 + other positive terms = 1001 + other positive terms

Since all remaining terms are positive, (1.1)¹⁰⁰⁰⁰ > 1000

(1.1)¹⁰⁰⁰⁰ is larger

Sequences and Series .

Permutations and Combinations .

The 14 chapters of Class 11 Mathematics .

The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Sequences and Series.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 7 NCERT book
- 80 marks, theory paper
- 3 quick checks
- Writing n terms instead of n + 1 terms in the expansion . Remember that the index r starts from 0 and ends at n, which makes the total count of terms n + 1.
- Ignoring the negative sign attached to the second term . Treat the expression (a - b)ⁿ as [a + (-b)]ⁿ so that powers of (-b) automatically produce alternating signs.
- Forgetting to raise numerical coefficients to powers . When a term is (2x)³, compute 2³ × x³ = 8x³ instead of writing 2x³.

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