Lesson: Finding a Specific Term Using the Binomial Theorem

In this lesson, we will learn how to find the term containing x^r and the term free of x by using the general term of a binomial expansion.

Worksheet: Finding a Specific Term Using the Binomial Theorem • 19 Questions

Q1:

Find the term independent of 𝑥 in the expansion of

Q2:

In the expansion of 6 𝑎 + 1 𝑎 2 7 , determine the term that has 𝑎 2 .

Q3:

Find the term free of 𝑧 in 𝑧 + 1 9 𝑧 3 1 2 .

Q4:

Is there a term free of 𝑥 in the expansion of 𝑥 + 8 𝑥 5 1 8 ?

Q5:

Find the term independent of 𝑥 in the expansion of

Q6:

Find the term containing 𝑥 1 4 in the expansion of

Q7:

Find the term that includes 𝑎 8 in 𝑎 + 1 𝑎 𝑎 + 1 𝑎 2 2 1 0 1 0 .

Q8:

Find the term independent of 𝑎 in the expansion of 𝑎 + 1 𝑎 𝑎 + 1 𝑎 .

Q9:

What is the term independent of 𝑥 in the expansion of 1 𝑥 𝑥 + 1 𝑥 ?

Q10:

Determine the value of the term independent of 𝑥 in the expansion of 𝑥 𝑥 + 1 𝑥 5 2 8 .

Q11:

Determine the order of the term free of 𝑥 in the expansion of 𝑥 + 1 𝑥 2 6 𝑛 , and find its value when 𝑛 = 2 .

Q12:

Consider the expansion of 𝑥 + 2 𝑥 𝑘 8 . Determine all the values of 𝑘 such that the expansion has a constant term (a term free from 𝑥 ).

Q13:

Given that the sixth term in the expansion of is independent of 𝑥 , find 𝑛 and the value of the sixth term.

Q14:

Find the term free of 𝑦 in 𝑦 + 1 6 𝑦 3 2 0 .

Q15:

Find the term that includes 𝑧 1 2 in 𝑧 + 1 𝑧 𝑧 + 1 𝑧 2 2 1 4 1 4 .

Q16:

Find the term that includes 𝑤 1 2 in 𝑤 + 1 𝑤 𝑤 + 1 𝑤 2 2 1 4 1 4 .

Q17:

Find the term that includes 𝑘 1 2 in 𝑘 + 1 𝑘 𝑘 + 1 𝑘 2 2 1 6 1 6 .

Q18:

In the expansion of 7 𝑎 + 1 𝑎 2 6 , determine the term that has 𝑎 3 .

Q19:

In the expansion of 5 𝑎 + 1 𝑎 2 6 , determine the term that has 𝑎 3 .

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