Lesson Worksheet: The Binomial Theorem Mathematics

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

Q1:

Use the binomial theorem to find the expansion of (1+𝑥).

  • A1+4𝑥+6𝑥+4𝑥+𝑥
  • B1+𝑥
  • C1+4𝑥+6𝑥+4𝑥+4𝑥
  • D𝑥+4𝑥+4𝑥+𝑥
  • E1+3𝑥+6𝑥+10𝑥+15𝑥

Q2:

Expand 𝑥2.

  • A𝑥+32𝑥6𝑥+22
  • B𝑥32𝑥+6𝑥22
  • C𝑥+32𝑥+6𝑥+22
  • D𝑥32𝑥+6𝑥22

Q3:

Expand 𝑥41𝑥.

  • A𝑥1,0245𝑥256+5𝑥3258𝑥+54𝑥1𝑥
  • B𝑥20𝑥+160𝑥640𝑥+1,280𝑥1,024
  • C𝑥20𝑥+160𝑥640𝑥+1,280𝑥1,024𝑥
  • D𝑥5𝑥+10𝑥10𝑥+5𝑥1𝑥

Q4:

Find the value of 𝑥 that satisfies 1+73𝑥+7×69(2)!𝑥+7×6×527(3)!𝑥++12,187𝑥=2,187.

Q5:

Find the value of 𝐶+𝐶+𝐶++𝐶.

Q6:

Using the binomial theorem, approximate to three decimal places the value of (1.05).

Q7:

Evaluate 3+1+31 using the binomial expansion theorem.

  • A36
  • B273
  • C12
  • D27
  • E123

Q8:

Use the binomial theorem to expand 2𝑥34𝑦5.

  • A16𝑥81+128𝑥𝑦135128𝑥𝑦75+512𝑥𝑦375256𝑦625
  • B16𝑥81128𝑥𝑦135+128𝑥𝑦75128𝑥𝑦375+256𝑦625
  • C16𝑥81128𝑥𝑦135+128𝑥𝑦75+512𝑥𝑦375+256𝑦625
  • D16𝑥81128𝑥𝑦135+128𝑥𝑦75512𝑥𝑦375+256𝑦625
  • E16𝑥81+128𝑥𝑦135+128𝑥𝑦75+512𝑥𝑦375+256𝑦625

Q9:

Using the binomial theorem, expand 𝑥2𝑥+1𝑥+2𝑥+1+2𝑥.

  • A𝑥+4𝑥+6𝑥+4𝑥+1
  • B𝑥4𝑥+6𝑥4𝑥+1
  • C𝑥+4𝑥+6𝑥+4𝑥+1
  • D𝑥4𝑥+6𝑥4𝑥+1

Q10:

Simplify 𝐶+17×𝐶+17×𝐶++17×𝐶++17×𝐶.

  • A19
  • B16
  • C18
  • D17
  • E15

This lesson includes 43 additional questions and 341 additional question variations for subscribers.

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