Binomial Theorem Practice Set
1. Write the expansion of (𝑥 + 𝑧)4 using binomial notation.
2. Use the binomial theorem to expand (1 + 𝑥)2 .
3. Expand (3 − 𝑦)3 using the binomial theorem.
4. Expand (𝑚 + 2𝑛)2 using binomial expansion.
5. Find the coefficient of x in (𝑥 + 1)5 .
6. Expand (2 + 𝑥)4 using the binomial theorem.
1 4
7. Expand (𝑥 − 𝑥) .
8. Write the first four terms of (3 + 2𝑏)6 in ascending powers of b.
1 5
𝑥
9. In the expansion of (𝑥 3 + 3 ) , find the term containing 𝑥 0 .
1 6
10. Find the term in 𝑥 2 in the expansion of (𝑥 2 + 𝑥) .
11. Write down and simplify the first three terms in ascending powers of b in (1 − 3𝑏)5.
12. Expand the first three terms of (2𝑏 + 1)4 in ascending powers of b.
13. If (𝑘 + 𝑝)4 is expanded, find the value of k such that coefficients of p and 𝑝2 are equal.
𝑥 5
2
14. Expand the first three terms of (1 + ) , then use to estimate 1.015.
15. Expand (1 + 𝑥 2 )6 and find the coefficient of 𝑥 4 .
1 6
16. Find the constant term in the expansion of (𝑥 2 + 𝑥) .
1 5
17. Expand (1 + 𝑥 2 ) and find the coefficient of 𝑥 −4 .
1 5
18. Find the term independent of x in (2𝑥 2 + 𝑥) .
19. Sally invests $600 at 1.5% interest for 10 years. Use binomial expansion (first 3 terms)
to estimate final amount.
20. In the expansion of (3 − 𝑞𝑥)5 + (𝑥 + 4)6 , find q∈ℤ such that the coefficient of 𝑥 2 is
700.