Binomial Theorem — Class 11 Mathematics
Core Concept
For a positive integer n, (a+b)^n=Σ ⁿCᵣ aⁿ⁻ʳbʳ. The general term is Tᵣ₊₁=ⁿCᵣaⁿ⁻ʳbʳ.
Worked Examples
(x+2)³=x³+6x²+12x+8.
In (x+2)^5, the term containing x³ is obtained with r=2: ⁵C₂x³2²=40x³.
Explained MCQs
- The coefficient of x² in (x+1)^4 is 6.
- There are n+1 terms in the expansion of (a+b)^n.
- The middle term depends on whether n is even or odd.
Practice
- Expand (2x−3)⁴.
- Find the coefficient of x³ in (1+x)^7.