Worksheet: Finding a Specific Coefficient Using the Binomial Theorem

Q1:

Determine the coefficient of in the expansion of .

• A
• B
• C0
• D

Q2:

Answer the following questions for the expansion of .

Given that the coefficient of is 160, and is positive, find .

• A
• B
• C
• D
• E

Hence, using your value of , work out the first three terms in ascending powers of in the expansion.

• A
• B
• C
• D
• E

Q3:

Find the coefficient of in the expansion of , where .

• A
• B
• C
• D

Q4:

In the expansion of a binomial, determine which of the following is equivalent to the relation .

• A
• B
• C
• D

Q5:

Consider the expansion of . Is the coefficient of nonzero?

• Ayes
• Bno

Q6:

Find the coefficient of in the expansion of .

Q7:

In the expansion of in ascending powers of , denotes the th term.

If, in the expansion of , the coefficients of and are equal, which of the following describes the possible values of ?

• A or
• B or
• C or
• D or

Q8:

Find the coefficient of in the expansion of .

• A
• B
• C
• D
• E

Q9:

In an expansion, if coefficient of coefficient of coefficient of , find .

• A56, 62
• B47, 56
• C82, 56
• D47, 62

Q10:

Consider the expansion of . Find all possible values of such that the coefficients of and are equal.

• A2, 4
• B2, 1
• C3, 1
• D3, 2

Q11:

Find the coefficient of in the expansion of .

Q12:

If the order of the term free of in is equal to the term free of in , find .

Q13:

Find the coefficient of the term in the expansion of .

• A
• B
• C
• D
• E

Q14:

Use Pascalβs triangle to determine the coefficients of the terms that result from the expansion of .

• A
• B
• C
• D
• E

Q15:

Determine the coefficient of in the expansion of .

Q16:

Determine the coefficient of in the expansion of .

Q17:

Consider the expansion of in descending powers of . Given that the coefficient of the third term is , find all possible values of .

• A
• B
• C
• D
• E

Q18:

Find the coefficient of in the expansion of .

Q19:

Find the coefficient of in the expansion of .

Q20:

In the expansion of , if the coefficient of the middle term equals the coefficient of , find the value of .

• A3
• B
• C
• D

Q21:

Find the coefficient of in .

• A
• B
• C
• D
• E

Q22:

Find the coefficient of in the expansion of .

Q23:

Find the coefficient of in .

Q24:

Find the coefficient of in the expansion of .

Q25:

The coefficient of in the expansion of is 144. Find the value of .

• A
• B
• C
• D
• E