# Worksheet: The Binomial Theorem

Q1:

Expand .

• A
• B
• C
• D

Q2:

Find the coefficient of in the expansion of .

Q3:

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?

• A10
• B12
• C
• D

Q4:

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 .

Q5:

Use the binomial theorem to find the expansion of .

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• B
• C
• D
• E

Q6:

Given that and , find the values of and where .

• A ,
• B ,
• C ,
• D ,

Q7:

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.

• A
• B
• C12
• D384
• E

Q8:

Find the third term in the expansion of .

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• D

Q9:

Find the third term in the expansion of .

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• D

Q10:

Expand .

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• D

Q11:

Expand .

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• D

Q12:

Expand .

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• D

Q13:

Expand .

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• D

Q14:

Answer the following questions for the expansion of .

Given that the coefficient of is , find .

• A
• B
• C
• D
• E

Hence, work out the value of the coefficient of .

Q15:

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

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• D

Q16:

Use the binomial theorem to find the expansion of .

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• D
• E

Q17:

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

Q18:

Find the two middle terms in the expansion of .

• A ,
• B ,
• C ,
• D ,

Q19:

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

• A14
• B8
• C6
• D4

Q20:

Which of the following is equal to

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• D
• E

Q21:

Which of the following is equal to

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• E

Q22:

Evaluate using the binomial expansion theorem.

• A36
• B12
• C
• D
• E27

Q23:

Use the binomial theorem to expand .

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• C
• D
• E

Q24:

Use the binomial theorem to find the expansion of .

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• B
• C
• D
• E

Q25:

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

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• D
• E