The Binomial Theorem Worksheets
Use combinations, ordered arrangements and explicitly approximate normal-distribution rules.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
Find the coefficient of x^3 in (1 + x)^6.
- Use n choose k = n! / (k!(n − k)!).
Answer: 20
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Find the coefficient of x^2 in (1 + x)^5.
2
Find the coefficient of x^3 in (1 + x)^7.
3
Find the coefficient of x^2 in (1 + x)^4.
4
Find the coefficient of x^2 in (1 + x)^9.
5
Find the coefficient of x^3 in (1 + x)^8.
6
Find the coefficient of x^3 in (1 + x)^5.
Answer Key
1. 102. 353. 64. 365. 566. 10