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).

  • A4𝑥6𝑥𝑦4𝑦
  • B4𝑥10𝑥𝑦+4𝑦
  • C4𝑥+6𝑥𝑦+4𝑦
  • D4𝑥6𝑥𝑦+4𝑦
  • E4𝑥10𝑥𝑦+4𝑦

Q2:

Expand the product (𝑝+4)(𝑞+6).

  • A𝑝𝑞+6𝑝+4𝑞+24
  • B2𝑝𝑞+6𝑝+4𝑞+24
  • C𝑝𝑞+4𝑝+6𝑞+24
  • D𝑝+𝑞+24
  • E𝑝𝑞+24

Q3:

Expand the product (𝑥4)(𝑥6).

  • A𝑥10𝑥+24
  • B𝑥4𝑥+24
  • C9𝑥+24
  • D𝑥10𝑥24
  • E𝑥+24

Q4:

Expand the product (𝑥+4)(𝑥+6).

  • A𝑥+24
  • B𝑥+10𝑥
  • C11𝑥+24
  • D𝑥+10𝑥+24
  • E𝑥+34𝑥

Q5:

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

  • A2𝑥𝑦+2𝑦𝑧
  • B2𝑥𝑦2𝑦𝑧
  • C2𝑥𝑦4𝑥𝑧+𝑥𝑦2𝑦𝑧
  • D2𝑥𝑦+4𝑥𝑧𝑥𝑦+2𝑦𝑧
  • E2𝑥𝑦+2𝑥𝑧+𝑥𝑦2𝑦𝑧

Q6:

Expand the product (3𝑚2)(𝑛+6𝑝).

  • A3𝑚𝑛+18𝑚𝑝2𝑛12𝑝
  • B3𝑚𝑛12𝑛𝑝
  • C3𝑚𝑛+18𝑚2𝑛12𝑝
  • D3𝑚+18𝑚𝑝2𝑛12𝑝
  • E3𝑚𝑛+18𝑚𝑝2𝑛𝑝

Q7:

Expand the product (2𝑥+1)(3𝑥2).

  • A6𝑥+𝑥2
  • B6𝑥𝑥2
  • C7𝑥2
  • D6𝑥𝑥+2
  • E6𝑥2

Q8:

Expand (2𝑎+3)(𝑏+4).

  • A2𝑎𝑏+8𝑎+3𝑏+12
  • B2𝑎𝑏+12
  • C𝑎𝑏+6𝑎+3𝑏+7
  • D2𝑎𝑏+8𝑎+3𝑏+7
  • E2𝑎𝑏+6𝑎+3𝑏+12

Q9:

Expand the product (𝑥+6)(𝑥4).

  • A𝑥+2𝑥+24
  • B𝑥24
  • C2𝑥+2𝑥24
  • D𝑥+2𝑥24
  • E3𝑥24

Q10:

Simplify 3𝑎22𝑎+4.

  • A6𝑎12𝑎4𝑎8
  • B6𝑎12𝑎+4𝑎8
  • C6𝑎+12𝑎4𝑎+8
  • D6𝑎+12𝑎4𝑎8
  • E6𝑎+12𝑎+4𝑎8

Q11:

Expand and simplify (𝑏+4)(5𝑏).

  • A𝑏+20𝑏+1
  • B𝑏+9𝑏+20
  • C𝑏+𝑏+20
  • D𝑏+9𝑏+20
  • E𝑏+𝑏+20

Q12:

Expand and simplify (2𝑎3)(3𝑎+5).

  • A5𝑎+19𝑎15
  • B6𝑎+𝑎15
  • C6𝑎15𝑎+1
  • D6𝑎+19𝑎15
  • E5𝑎+𝑎15

Q13:

Expand and simplify (2𝑚2)(6𝑚)+4(𝑚5).

  • A2𝑚+18𝑚32
  • B2𝑚+14𝑚17
  • C2𝑚+14𝑚32
  • D2𝑚+18𝑚32
  • E2𝑚+14𝑚32

Q14:

Expand and simplify 7(3𝑦)(𝑦+2).

  • A𝑦+𝑦1
  • B𝑦𝑦1
  • C𝑦𝑦1
  • D𝑦𝑦+1
  • E𝑦𝑦+1

Q15:

Simplify (8𝑦+3)(2𝑦+1).

  • A16𝑦14𝑦+3
  • B16𝑦+14𝑦3
  • C16𝑦+16𝑦+3
  • D16𝑦14𝑦3
  • E16𝑦+14𝑦+3

Q16:

Expand and simplify (𝑎+4)(2)(𝑎+8).

  • A2𝑎24𝑎64
  • B2𝑎+24𝑎+64
  • C2𝑎+12𝑎+32
  • D𝑎+12𝑎+32
  • E𝑎24𝑎64

Q17:

Find 𝐴𝐵 given 𝐴=5𝑥3𝑥 and 𝐵=6𝑥+3𝑥.

  • A30𝑥15𝑥+18𝑥9𝑥
  • B30𝑥+15𝑥+18𝑥+9𝑥
  • C30𝑥+15𝑥18𝑥9𝑥
  • D30𝑥+15𝑥18𝑥+9𝑥
  • E30𝑥+15𝑥+18𝑥9𝑥

Q18:

Find 𝐴𝐵 given 𝐴=8𝑥+2 and 𝐵=5𝑥1.

  • A40𝑥+2𝑥+2
  • B40𝑥2𝑥+2
  • C48𝑥+2𝑥2
  • D40𝑥+2𝑥2
  • E40𝑥2𝑥2

Q19:

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

  • A72𝑥𝑦𝑦
  • B72𝑥𝑦72𝑥𝑦
  • C72𝑥𝑦+72𝑥𝑦
  • D72𝑥𝑦

Q20:

Expand and simplify (2𝑥+3)(2𝑥4).

  • A4𝑥+2𝑥+12
  • B4𝑥14𝑥12
  • C4𝑥2𝑥12
  • D4𝑥+2𝑥12
  • E4𝑥14𝑥12

Q21:

Expand the product (2𝑚+𝑛)(2𝑚𝑛).

  • A4𝑚2𝑚𝑛+𝑛
  • B4𝑚+𝑛
  • C4𝑚𝑛
  • D4𝑚+2𝑚𝑛+𝑛
  • E4𝑚+2𝑚𝑛𝑛

Q22:

Expand the product (𝑥+4)(𝑥+6).

  • A𝑥+10𝑥+24
  • B𝑥+10𝑥
  • C𝑥+24
  • D𝑥+34𝑥
  • E11𝑥+24

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.

  • A32𝑥+20𝑥3
  • B32𝑥4𝑥3
  • C12𝑥20𝑥3
  • D12𝑥4𝑥3
  • E32𝑥+4𝑥3

Q24:

Expand the product (𝑥+6)(𝑥4).

  • A𝑥24
  • B𝑥+2𝑥+24
  • C𝑥+2𝑥24
  • D3𝑥24
  • E2𝑥+2𝑥24

Q25:

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

  • A3𝑎49
  • B6𝑎14
  • C9𝑎49
  • D9𝑎49
  • E9𝑎7

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