The Binomial Theorem

Pascal's triangle, the general term C(n, k)·aⁿ⁻ᵏ·bᵏ, and finding a particular term or coefficient.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

• math30 1 binomial theorem

The questions

1. Counting the top 1 as row 0, which is row 5 of Pascal's triangle?
2. How many terms are in the expansion of (x + y)⁹?
3. In the expansion of (a + b)⁷, what is the coefficient of a⁴b³?
4. Which expression gives the general term, the (k + 1)th term, of (x + 2)⁶ written in descending powers of x?
5. What is the coefficient of the third term in the expansion of (x + 3)⁵, written in descending powers of x?
6. Which is the term containing x² in the expansion of (x + 2)⁵?
7. What is the constant term in the expansion of (x + 1/x)⁶?
8. What is the term containing x³ in the expansion of (2x − 1)⁴?
9. What is the sum of the coefficients in the expansion of (x + y)⁸?
10. In the expansion of (x + a)⁵, where a > 0, the coefficient of x³ is 40. What is the value of a?

Answer these free