# Worksheet: The Binomial Theorem

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

**Q3: **

Use the binomial theorem to find the expansion of .

- A
- B
- C
- D
- E

**Q4: **

Use the binomial theorem to find the expansion of .

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- B
- C
- D
- E

**Q5: **

Find the third term in the expansion of .

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- B
- C
- D

**Q6: **

Consider the expansion of Given that the constant of this expansion is 720, find all the possible values of .

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- D

**Q7: **

Which of the following is equal to

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**Q8: **

Write the coefficients of the terms that result from the expansion of .

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**Q9: **

Use the binomial theorem to expand .

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- B
- C
- D
- E

**Q10: **

Expand .

- A
- B
- C
- D

**Q11: **

Evaluate using the binomial expansion theorem.

- A36
- B
- C12
- D27
- E

**Q12: **

Expand .

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- B
- C
- D

**Q13: **

Expand .

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- D

**Q14: **

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

- A8
- B6
- C14
- D4

**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 .

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- 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 .

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- D

**Q22: **

Expand .

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- E

**Q23: **

Expand .

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- D

**Q25: **

Find the value of that satisfies