Worksheet: Multiplying Binomials

In this worksheet, we will practice multiplying two binomials using different methods such as FOIL or the vertical method.

Q1:

Expand and simplify (2𝑥4𝑦)(2𝑥𝑦).

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

Q2:

Expand the product (𝑝+4)(𝑞+6).

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

Q3:

Expand the product (𝑥4)(𝑥6).

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

Q4:

Expand the product (𝑥+4)(𝑥+6).

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

Q5:

Use the distributive property to fully expand (2𝑥+𝑦)(𝑥𝑦2𝑧).

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

Q6:

Expand the product (3𝑚2)(𝑛+6𝑝).

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

Q7:

Expand the product (2𝑥+1)(3𝑥2).

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

Q8:

Expand (2𝑎+3)(𝑏+4).

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

Q9:

Expand the product (𝑥+6)(𝑥4).

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

Q10:

Simplify 3𝑎22𝑎+4.

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

Q11:

Expand and simplify (𝑏+4)(5𝑏).

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

Q12:

Expand and simplify (2𝑎3)(3𝑎+5).

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

Q13:

Expand and simplify (2𝑚2)(6𝑚)+4(𝑚5).

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

Q14:

Expand and simplify 7(3𝑦)(𝑦+2).

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

Q15:

Simplify (8𝑦+3)(2𝑦+1).

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

Q16:

Expand and simplify (𝑎+4)(2)(𝑎+8).

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

Q17:

Find 𝐴𝐵 given 𝐴=5𝑥3𝑥 and 𝐵=6𝑥+3𝑥.

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

Q18:

Find 𝐴𝐵 given 𝐴=8𝑥+2 and 𝐵=5𝑥1.

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

Q19:

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

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

Q20:

Expand and simplify (2𝑥+3)(2𝑥4).

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

Q21:

Expand the product (2𝑚+𝑛)(2𝑚𝑛).

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

Q22:

Expand the product (𝑥+4)(𝑥+6).

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

Q23:

A developer wants to purchase a plot of land whose area can be described by the following expression: (4𝑥+1)(8𝑥3). Multiply the binomials to find the area of the plot as a polynomial in standard form.

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

Q24:

Expand the product (𝑥+6)(𝑥4).

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

Q25:

Use the difference of two squares identity to expand (3𝑎+7)(3𝑎7).

  • A 3 𝑎 4 9
  • B 6 𝑎 1 4
  • C 9 𝑎 4 9
  • D 9 𝑎 4 9
  • E 9 𝑎 7

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.