# Worksheet: The Binomial Theorem

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

Q1:

Use the binomial theorem to find the expansion of .

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• E

Q2:

Expand .

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• D

Q3:

Use the binomial theorem to find the expansion of .

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• E

Q4:

Use the binomial theorem to find the expansion of .

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Q5:

Find the third term in the expansion of .

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• 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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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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Q10:

Expand .

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Q11:

Evaluate using the binomial expansion theorem.

• A36
• B
• C12
• D27
• E

Q12:

Expand .

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Q13:

Expand .

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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 .

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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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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 .

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• B ,
• C ,
• D ,

Q21:

Expand .

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Q22:

Expand .

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Q23:

Expand .

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Q24:

Find the third term in the expansion of .

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Q25:

Find the value of that satisfies