Class 11 Maths Chapter 7 Binomial Theorem – Revision Notes

The binomial theorem gives a formula for expanding powers like (a+b)^n without multiplying everything out term by term. Class 11 Maths Chapter 7 covers the general term, the Pascal’s triangle pattern behind the coefficients, and how to locate the middle term of an expansion.

Last Updated: September 23, 2026

Binomial Theorem

• (a+b)ⁿ = ∑ⁿC_ka^n−kb^k, k=0 to n.

General Term

• T_k+1 = ⁿC_ka^n−kb^k.

Properties

• n+1 terms total.
• Symmetric: ⁿC_k=ⁿC_n−k.
• Sum of coefficients = 2ⁿ.
• Pascal’s Triangle: each entry = sum of two above.

Middle Term

• n even: 1 middle term ((n/2)+1)th.
• n odd: 2 middle terms.

One-Line Summary

The binomial theorem expands (a+b)ⁿ using binomial coefficients (from Pascal’s Triangle), with the general term formula allowing any specific term to be found directly without full expansion.

Frequently Asked Questions

What does the Binomial Theorem actually help calculate?
It gives a formula to expand expressions of the form (a+b) raised to the power n for any positive integer n without multiplying the binomial by itself repeatedly, using binomial coefficients for each term.

What is the significance of the general term in a binomial expansion?
The general term lets us find any specific term, such as the middle term or a term with a given power, directly, without writing out the entire expansion.

Written by Satish

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