Worksheet: Using Area Models to Multiply Polynomials

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 ) ( 𝑥 𝑦 ) .

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

Q2:

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

  • A 𝑎 + 2 𝑎 𝑏 + 𝑏
  • B 𝑎 + 𝑏
  • C 𝑎 + 2 𝑎 𝑏 + 𝑏
  • D 𝑎 + 2 𝑎 𝑏 + 𝑏
  • E 𝑎 + 2 𝑎 𝑏 + 𝑏

Q3:

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

  • A 3 𝑎 𝑏 + 2 𝑐 𝑑
  • B 3 𝑎 𝑏 + 2 𝑎 𝑐 𝑎 𝑑
  • C 3 𝑎 𝑏 + 6 𝑎 𝑐 + 3 𝑎 𝑑
  • D 3 𝑎 𝑏 + 6 𝑐 3 𝑑
  • E 3 𝑎 𝑏 + 6 𝑎 𝑐 3 𝑎 𝑑

Q4:

Use an area model to write an expression equivalent to ( 4 𝑎 + 𝑏 ) ( 3 2 𝑏 𝑎 ) .

  • A 1 2 𝑎 9 𝑎 𝑏 4 𝑎 + 3 𝑏 2 𝑏
  • B 1 2 𝑎 9 𝑎 𝑏 4 𝑎 + 3 𝑏 2 𝑏
  • C 1 2 𝑎 + 7 𝑎 𝑏 + 4 𝑎 + 3 𝑏 2 𝑏
  • D 1 2 𝑎 + 9 𝑎 𝑏 + 4 𝑎 + 3 𝑏 2 𝑏
  • E 1 2 𝑎 + 7 𝑎 𝑏 + 4 𝑎 + 3 𝑏 2 𝑏

Q5:

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

  • A ( 4 𝑦 2 𝑥 ) 2 𝑦 + 𝑥 2 3 = 8 𝑦 2 𝑥 𝑦 1 2 𝑦 𝑥 6 𝑥
  • B ( 4 𝑦 2 𝑥 ) 2 𝑦 + 2 𝑥 3 = 8 𝑦 4 𝑥 𝑦 1 2 𝑦 4 + 6 𝑥 + 8 𝑦 𝑥
  • C ( 4 𝑦 2 𝑥 ) 2 𝑦 + 𝑥 2 3 = 8 𝑦 2 𝑥 𝑦 1 2 𝑦 𝑥 6 𝑥
  • D ( 4 𝑦 2 𝑥 ) 2 𝑦 + 𝑥 2 3 = 8 𝑦 2 𝑥 𝑦 1 2 𝑦 𝑥 + 6 𝑥
  • E ( 4 𝑦 2 𝑥 ) 2 𝑦 + 𝑥 2 3 = 8 𝑦 2 𝑥 𝑦 1 2 𝑦 𝑥 + 6 𝑥

Q6:

Use an area model to write an expression equivalent to ( 2 𝑥 7 ) ( 3 𝑦 + 2 𝑥 ) .

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

Q7:

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

  • A ( 4 𝑎 + 5 ) ( 𝑎 3 ) = 4 𝑎 7 𝑎 1 5
  • B ( 4 𝑎 5 ) ( 𝑎 + 3 ) = 4 𝑎 + 7 𝑎 1 5
  • C ( 𝑎 + 5 ) ( 4 𝑎 3 ) = 4 𝑎 + 1 7 𝑎 1 5
  • D ( 𝑎 + 5 ) ( 𝑎 3 ) = 𝑎 + 1 7 𝑎 1 5
  • E ( 𝑎 5 ) ( 4 𝑎 + 3 ) = 4 𝑎 1 7 𝑎 1 5

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