How to Calculate Binomial Expansion
What is Binomial Expansion?
Binomial expansion uses the binomial theorem to expand expressions like (a + b)ⁿ into a polynomial sum. Pascal's triangle or the formula with binomial coefficients provides all terms.
Formula
(a + b)ⁿ = Σ C(n,k) × aⁿ⁻ᵏ × bᵏ for k=0 to n
Step-by-Step Guide
- 1Input the binomial (a + b) and power n
- 2Calculate binomial coefficients C(n,k)
- 3Expand each term and sum them
Worked Examples
Input
(x + 2)³
Result
x³ + 6x² + 12x + 8
Using C(3,k) coefficients: 1, 3, 3, 1
Common Mistakes to Avoid
- ✕Incorrect binomial coefficients
- ✕Wrong power distribution in terms
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