Worksheet: Multiplying Polynomials Using Area Models

In this worksheet, we will practice using area models to multiply polynomials.

Q1:

Use an area model to write an expression equivalent to (𝑥+𝑦)(𝑥𝑦).

  • A𝑥+𝑦
  • B𝑥𝑦
  • C𝑥2𝑥𝑦𝑦
  • D𝑥2𝑥𝑦+𝑦
  • E𝑥+2𝑥𝑦𝑦

Q2:

Use an area model to write an expression equivalent to (𝑎+𝑏).

  • A𝑎+2𝑎𝑏+𝑏
  • B𝑎+2𝑎𝑏+𝑏
  • C𝑎+𝑏
  • D𝑎+2𝑎𝑏+𝑏
  • E𝑎+2𝑎𝑏+𝑏

Q3:

Use the area model to write an expression equivalent to 3𝑎(𝑏+2𝑐𝑑).

  • A3𝑎𝑏+6𝑐3𝑑
  • B3𝑎𝑏+2𝑐𝑑
  • C3𝑎𝑏+2𝑎𝑐𝑎𝑑
  • D3𝑎𝑏+6𝑎𝑐+3𝑎𝑑
  • E3𝑎𝑏+6𝑎𝑐3𝑎𝑑

Q4:

Use an area model to write an expression equivalent to (4𝑎+𝑏)(32𝑏𝑎).

  • A12𝑎+7𝑎𝑏+4𝑎+3𝑏2𝑏
  • B12𝑎9𝑎𝑏4𝑎+3𝑏2𝑏
  • C12𝑎+9𝑎𝑏+4𝑎+3𝑏2𝑏
  • D12𝑎+7𝑎𝑏+4𝑎+3𝑏2𝑏
  • E12𝑎9𝑎𝑏4𝑎+3𝑏2𝑏

Q5:

Which of the following equations is represented by the given area model?

  • A(4𝑦2𝑥)2𝑦+𝑥23=8𝑦2𝑥𝑦12𝑦𝑥+6𝑥
  • B(4𝑦2𝑥)2𝑦+𝑥23=8𝑦2𝑥𝑦12𝑦𝑥6𝑥
  • C(4𝑦2𝑥)2𝑦+2𝑥3=8𝑦4𝑥𝑦12𝑦4+6𝑥+8𝑦𝑥
  • D(4𝑦2𝑥)2𝑦+𝑥23=8𝑦2𝑥𝑦12𝑦𝑥+6𝑥
  • E(4𝑦2𝑥)2𝑦+𝑥23=8𝑦2𝑥𝑦12𝑦𝑥6𝑥

Q6:

Use an area model to write an expression equivalent to (2𝑥7)(3𝑦+2𝑥).

  • A6𝑥𝑦+4𝑥21𝑦+14𝑥
  • B6𝑥𝑦14𝑥
  • C6𝑥𝑦+4𝑥+21𝑦+14𝑥
  • D6𝑥𝑦+4𝑥+21𝑦14𝑥
  • E6𝑥𝑦+4𝑥21𝑦14𝑥

Q7:

Which of the following equations is represented by the given area model?

  • A(𝑎+5)(4𝑎3)=4𝑎+17𝑎15
  • B(𝑎5)(4𝑎+3)=4𝑎17𝑎15
  • C(4𝑎5)(𝑎+3)=4𝑎+7𝑎15
  • D(4𝑎+5)(𝑎3)=4𝑎7𝑎15
  • E(𝑎+5)(𝑎3)=𝑎+17𝑎15

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