# Worksheet: The Binomial Theorem

In this worksheet, we will practice on expanding any binomial expression of the form (a+b)^n.

**Q7: **

Which of the following is equal to

- A
- B
- C
- D
- E

**Q10: **

Expand .

- A
- B
- C
- D

**Q12: **

Expand .

- A
- B
- C
- D

**Q13: **

Expand .

- A
- B
- C
- D

**Q14: **

Find the coefficient of the fourth term in the expansion of .

**Q15: **

Answer the following questions for the expansion of .

Given that the coefficient of is 60, and is positive, find .

- A
- B
- C
- D
- E

Hence, using your value of , work out the coefficient of in the expansion.

- A12
- B
- C
- D384
- E

**Q16: **

Answer the following questions for the expansion of .

Given that the coefficient of is 189, find .

- A
- B
- C
- D
- E

Hence, work out the value of the coefficient of .

**Q17: **

Consider the expansion of in descending powers of . What are the possible values of it, if the third term in this expansion is equal to 640?

- A12
- B
- C
- D10

**Q18: **

Find the two middle terms in the expansion of .

- A,
- B,
- C,
- D,

**Q19: **

Find given that the ratio of the middle terms in the expansion of is .

**Q20: **

Given that and , find the values of and where .

- A,
- B,
- C,
- D,

**Q21: **

Expand .

- A
- B
- C
- D

**Q22: **

Expand .

- A
- B
- C
- D
- E

**Q23: **

Expand .

- A
- B
- C
- D

**Q25: **

Find the value of that satisfies