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Worksheet: Finding a Specific Term Using the Binomial Theorem

Q1:

Find the term free of 𝑧 in ο€Ό 𝑧 + 1 9 𝑧  3 1 2 .

  • A 5 5 8 1
  • B 2 2 2 4 3
  • C 2 2 0 2 7
  • D 2 2 0 7 2 9
  • E 2 2 9

Q2:

Find the term free of 𝑦 in ο€½ 𝑦 + 1 6 𝑦  3 2 0 .

  • A 1 6 1 5 3 2 4
  • B 1 6 1 5 2 5 9 2
  • C 2 5 8 4 5
  • D 3 2 3 1 6 2
  • E 3 2 3 2

Q3:

Find the term independent of π‘Ž in the expansion of ο€Ό π‘Ž + 1 π‘Ž  ο€Ό π‘Ž + 1 π‘Ž  2 2 1 2 1 2 .

Q4:

Is there a term free of π‘₯ in the expansion of ο€Ό π‘₯ + 8 π‘₯  5 1 8 ?

  • Ayes
  • Bno

Q5:

Given that the sixth term in the expansion of is independent of π‘₯ , find 𝑛 and the value of the sixth term.

  • A 𝑛 = 2 0 , sixth term is = βˆ’ 5 0 4
  • B 𝑛 = 5 , sixth term is = βˆ’ 1 2 6
  • C 𝑛 = 7 , sixth term is = βˆ’ 2 1
  • D 𝑛 = 1 0 , sixth term is βˆ’ 2 5 2

Q6:

Consider the expansion of ο€Ό π‘₯ + 2 π‘₯  π‘˜ 8 . Determine all the values of π‘˜ such that the expansion has a constant term (a term free from π‘₯ ).

  • A 1 , 3 , 7 , 8
  • B 7
  • C 1 , 2 , 3 , 4 , 5 , 6 , 7
  • D 1 , 3 , 7

Q7:

What is the term independent of π‘₯ in the expansion of

Q8:

Determine the value of the term independent of π‘₯ in the expansion of π‘₯ ο€Ό π‘₯ + 1 π‘₯  5 2 8 .

Q9:

Find the term that includes π‘Ž 8 in ο€Ό π‘Ž + 1 π‘Ž  βˆ’ ο€Ό π‘Ž + 1 π‘Ž  2 2 1 0 1 0 .

  • A 7 5 π‘Ž 8
  • B 1 1 9 π‘Ž 8
  • C 1 3 0 π‘Ž 8
  • D 1 1 0 π‘Ž 8
  • E 1 2 1 π‘Ž 8

Q10:

Find the term that includes 𝑧 1 2 in ο€Ό 𝑧 + 1 𝑧  βˆ’ ο€Ό 𝑧 + 1 𝑧  2 2 1 4 1 4 .

  • A 9 1 0 𝑧 1 2
  • B 1 0 0 0 𝑧 1 2
  • C 1 0 1 5 𝑧 1 2
  • D 9 8 7 𝑧 1 2
  • E 1 0 0 2 𝑧 1 2

Q11:

Find the term that includes 𝑀 1 2 in ο€Ό 𝑀 + 1 𝑀  βˆ’ ο€Ό 𝑀 + 1 𝑀  2 2 1 4 1 4 .

  • A 9 1 0 𝑀 1 2
  • B 1 0 0 0 𝑀 1 2
  • C 1 0 1 5 𝑀 1 2
  • D 9 8 7 𝑀 1 2
  • E 1 0 0 2 𝑀 1 2

Q12:

Find the term that includes π‘˜ 1 2 in ο€Ό π‘˜ + 1 π‘˜  βˆ’ ο€Ό π‘˜ + 1 π‘˜  2 2 1 6 1 6 .

  • A 3 8 0 8 π‘˜ 1 2
  • B 4 3 5 2 π‘˜ 1 2
  • C 4 4 8 8 π‘˜ 1 2
  • D 4 2 4 8 π‘˜ 1 2
  • E 4 3 8 4 π‘˜ 1 2

Q13:

Find the term independent of π‘₯ in the expansion of

Q14:

Determine the order of the term free of in the expansion of , and find its value when .

  • A
  • B
  • C
  • D

Q15:

In the expansion of ο€Ό 6 π‘Ž + 1 π‘Ž  2 7 , determine the term that has π‘Ž 2 .

  • A 7 5 6 π‘Ž 2
  • B 4 5 3 6 0 π‘Ž 2
  • C 2 1 0 π‘Ž 2
  • D 7 5 6 0 π‘Ž 2

Q16:

In the expansion of ο€Ό 7 π‘Ž + 1 π‘Ž  2 6 , determine the term that has π‘Ž 3 .

  • A 7 3 5 π‘Ž 3
  • B 3 6 0 1 5 π‘Ž 3
  • C 1 4 0 π‘Ž 3
  • D 6 8 6 0 π‘Ž 3
  • E 1 0 5 π‘Ž 3

Q17:

In the expansion of ο€Ό 5 π‘Ž + 1 π‘Ž  2 6 , determine the term that has π‘Ž 3 .

  • A 3 7 5 π‘Ž 3
  • B 9 3 7 5 π‘Ž 3
  • C 1 0 0 π‘Ž 3
  • D 2 5 0 0 π‘Ž 3
  • E 7 5 π‘Ž 3

Q18:

Find the term independent of π‘₯ in the expansion of

  • A 2 1 1 6
  • B84
  • C1
  • D 2 1 1 2 8
  • E 2 1 6 4

Q19:

Find the term containing π‘₯ 1 4 in the expansion of

  • A 2 π‘₯ 1 4
  • B 3 4 π‘₯ 1 4
  • C 2 8 8 π‘₯ 1 4
  • D 1 6 π‘₯ 1 4