Worksheet: Multiplying Binomials

In this worksheet, we will practice multiplying binomials with integer and fractional coefficients.

Q1:

Expand and simplify ( 2 𝑥 4 𝑦 ) ( 2 𝑥 𝑦 ) .

  • A 4 𝑥 1 0 𝑥 𝑦 + 4 𝑦 2 2
  • B 4 𝑥 1 0 𝑥 𝑦 + 4 𝑦 2 2
  • C 4 𝑥 6 𝑥 𝑦 4 𝑦 2 2
  • D 4 𝑥 6 𝑥 𝑦 + 4 𝑦 2 2
  • E 4 𝑥 + 6 𝑥 𝑦 + 4 𝑦 2 2

Q2:

Expand the product ( 𝑝 + 4 ) ( 𝑞 + 6 ) .

  • A 𝑝 𝑞 + 2 4
  • B 𝑝 𝑞 + 4 𝑝 + 6 𝑞 + 2 4
  • C 𝑝 + 𝑞 + 2 4
  • D 𝑝 𝑞 + 6 𝑝 + 4 𝑞 + 2 4
  • E 2 𝑝 𝑞 + 6 𝑝 + 4 𝑞 + 2 4

Q3:

Expand the product ( 𝑥 4 ) ( 𝑥 6 ) .

  • A 9 𝑥 + 2 4 2
  • B 𝑥 1 0 𝑥 2 4 2
  • C 𝑥 + 2 4 2
  • D 𝑥 1 0 𝑥 + 2 4 2
  • E 𝑥 4 𝑥 + 2 4 2

Q4:

Expand the product ( 𝑥 + 4 ) ( 𝑥 + 6 ) .

  • A 𝑥 + 3 4 𝑥 2
  • B 𝑥 + 2 4 2
  • C 1 1 𝑥 + 2 4 2
  • D 𝑥 + 1 0 𝑥 + 2 4 2
  • E 𝑥 + 1 0 𝑥 2

Q5:

Use the distributive property to fully expand ( 2 𝑥 + 𝑦 ) ( 𝑥 𝑦 2 𝑧 ) .

  • A 2 𝑥 𝑦 + 4 𝑥 𝑧 𝑥 𝑦 + 2 𝑦 𝑧 2 2
  • B 2 𝑥 𝑦 2 𝑦 𝑧 2
  • C 2 𝑥 𝑦 + 2 𝑦 𝑧 2
  • D 2 𝑥 𝑦 4 𝑥 𝑧 + 𝑥 𝑦 2 𝑦 𝑧 2 2
  • E 2 𝑥 𝑦 + 2 𝑥 𝑧 + 𝑥 𝑦 2 𝑦 𝑧 2 2

Q6:

Expand the product ( 3 𝑚 2 ) ( 𝑛 + 6 𝑝 ) .

  • A 3 𝑚 𝑛 + 1 8 𝑚 2 𝑛 1 2 𝑝
  • B 3 𝑚 + 1 8 𝑚 𝑝 2 𝑛 1 2 𝑝
  • C 3 𝑚 𝑛 + 1 8 𝑚 𝑝 2 𝑛 𝑝
  • D 3 𝑚 𝑛 + 1 8 𝑚 𝑝 2 𝑛 1 2 𝑝
  • E 3 𝑚 𝑛 1 2 𝑛 𝑝

Q7:

Expand the product ( 2 𝑥 + 1 ) ( 3 𝑥 2 ) .

  • A 6 𝑥 + 𝑥 2 2
  • B 6 𝑥 𝑥 + 2 2
  • C 7 𝑥 2 2
  • D 6 𝑥 𝑥 2 2
  • E 6 𝑥 2 2

Q8:

Expand ( 2 𝑎 + 3 ) ( 𝑏 + 4 ) .

  • A 2 𝑎 𝑏 + 1 2
  • B 2 𝑎 𝑏 + 8 𝑎 + 3 𝑏 + 7
  • C 2 𝑎 𝑏 + 6 𝑎 + 3 𝑏 + 1 2
  • D 2 𝑎 𝑏 + 8 𝑎 + 3 𝑏 + 1 2
  • E 𝑎 𝑏 + 6 𝑎 + 3 𝑏 + 7

Q9:

Expand the product ( 𝑥 + 6 ) ( 𝑥 4 ) .

  • A 𝑥 2 4 2
  • B 𝑥 + 2 𝑥 + 2 4 2
  • C 3 𝑥 2 4
  • D 𝑥 + 2 𝑥 2 4 2
  • E 2 𝑥 + 2 𝑥 2 4 2

Q10:

Simplify 3 𝑎 2 2 𝑎 + 4 3 2 .

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

Q11:

Expand and simplify ( 𝑏 + 4 ) ( 5 𝑏 ) .

  • A 𝑏 + 9 𝑏 + 2 0 2
  • B 𝑏 + 𝑏 + 2 0 2
  • C 𝑏 + 9 𝑏 + 2 0 2
  • D 𝑏 + 𝑏 + 2 0 2
  • E 𝑏 + 2 0 𝑏 + 1 2

Q12:

Expand and simplify ( 2 𝑎 3 ) ( 3 𝑎 + 5 ) .

  • A 5 𝑎 + 𝑎 1 5 2
  • B 6 𝑎 1 5 𝑎 + 1 2
  • C 6 𝑎 + 1 9 𝑎 1 5 2
  • D 6 𝑎 + 𝑎 1 5 2
  • E 5 𝑎 + 1 9 𝑎 1 5 2

Q13:

Expand and simplify ( 2 𝑚 2 ) ( 6 𝑚 ) + 4 ( 𝑚 5 ) .

  • A 2 𝑚 + 1 4 𝑚 1 7 2
  • B 2 𝑚 + 1 4 𝑚 3 2 2
  • C 2 𝑚 + 1 8 𝑚 3 2 2
  • D 2 𝑚 + 1 8 𝑚 3 2 2
  • E 2 𝑚 + 1 4 𝑚 3 2 2

Q14:

Expand and simplify 7 ( 3 𝑦 ) ( 𝑦 + 2 ) .

  • A 𝑦 𝑦 + 1 2
  • B 𝑦 𝑦 1 2
  • C 𝑦 𝑦 1 2
  • D 𝑦 𝑦 + 1 2
  • E 𝑦 + 𝑦 1 2

Q15:

Simplify ( 8 𝑦 + 3 ) ( 2 𝑦 + 1 ) .

  • A 1 6 𝑦 + 1 4 𝑦 3 2
  • B 1 6 𝑦 1 4 𝑦 + 3 2
  • C 1 6 𝑦 1 4 𝑦 3 2
  • D 1 6 𝑦 + 1 4 𝑦 + 3 2
  • E 1 6 𝑦 + 1 6 𝑦 + 3 2

Q16:

Expand and simplify ( 𝑎 + 4 ) ( 2 ) ( 𝑎 + 8 ) .

  • A 𝑎 + 1 2 𝑎 + 3 2 2
  • B 2 𝑎 + 1 2 𝑎 + 3 2 2
  • C 𝑎 2 4 𝑎 6 4 2
  • D 2 𝑎 2 4 𝑎 6 4 2
  • E 2 𝑎 + 2 4 𝑎 + 6 4 2

Q17:

Find 𝐴 𝐵 given 𝐴 = 5 𝑥 3 𝑥 3 and 𝐵 = 6 𝑥 + 3 𝑥 2 .

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

Q18:

Find 𝐴 𝐵 given 𝐴 = 8 𝑥 + 2 and 𝐵 = 5 𝑥 1 .

  • A 4 0 𝑥 + 2 𝑥 + 2 2
  • B 4 8 𝑥 + 2 𝑥 2 2
  • C 4 0 𝑥 2 𝑥 2 2
  • D 4 0 𝑥 + 2 𝑥 2 2
  • E 4 0 𝑥 2 𝑥 + 2 2

Q19:

Given that 𝑎 = 8 𝑥 , 𝑏 = 9 𝑥 𝑦 , and 𝑐 = 𝑥 𝑦 , express 𝑎 𝑏 𝑐 in terms of 𝑥 and 𝑦 .

  • A 7 2 𝑥 𝑦 𝑦 3
  • B 7 2 𝑥 𝑦 + 7 2 𝑥 𝑦 3 2 2
  • C 7 2 𝑥 𝑦 2
  • D 7 2 𝑥 𝑦 7 2 𝑥 𝑦 3 2 2

Q20:

Expand and simplify ( 2 𝑥 + 3 ) ( 2 𝑥 4 ) .

  • A 4 𝑥 1 4 𝑥 1 2 2
  • B 4 𝑥 1 4 𝑥 1 2 2
  • C 4 𝑥 + 2 𝑥 + 1 2 2
  • D 4 𝑥 + 2 𝑥 1 2 2
  • E 4 𝑥 2 𝑥 1 2 2

Q21:

Expand the product ( 2 𝑚 + 𝑛 ) ( 2 𝑚 𝑛 ) .

  • A 4 𝑚 + 2 𝑚 𝑛 𝑛 2 2
  • B 4 𝑚 + 2 𝑚 𝑛 + 𝑛 2 2
  • C 4 𝑚 2 𝑚 𝑛 + 𝑛 2 2
  • D 4 𝑚 𝑛 2 2
  • E 4 𝑚 + 𝑛 2 2

Q22:

Expand the product ( 𝑥 + 4 ) ( 𝑥 + 6 ) .

  • A 𝑥 + 3 4 𝑥 2
  • B 𝑥 + 2 4 2
  • C 1 1 𝑥 + 2 4 2
  • D 𝑥 + 1 0 𝑥 + 2 4 2
  • E 𝑥 + 1 0 𝑥 2

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