Worksheet: Evaluating Algebraic Expressions by Factoring Out the Highest Common Factor

In this worksheet, we will practice evaluating algebraic expressions by factoring out the highest common factor.

Q1:

If 3 𝑝 + 2 𝑞 = 4 and 6 𝑎 5 𝑏 = 1 0 , what is the value of 2 0 ( 𝑞 + 𝑏 ) + 6 ( 5 𝑝 4 𝑎 ) ?

  • A 1 4 0
  • B80
  • C140
  • D0
  • E 8 0

Q2:

Given that 𝑎 𝑏 4 𝑐 + 2 𝑎 = 1 2 , what is the value of 1 2 𝑐 3 𝑎 𝑏 6 𝑎 ?

  • A 3 6
  • B36
  • C32
  • D 2 4
  • E24

Q3:

If 5 𝑑 3 𝑓 = 3 and 2 𝑝 + 3 𝑑 = 4 , what is the value of 1 2 𝑑 + 6 𝑓 1 0 𝑑 + 8 𝑝 ?

  • A 1 2
  • B 2 2
  • C10
  • D12
  • E 1 0

Q4:

Given that 3 𝑚 4 𝑛 = 2 , what is the value of 6 𝑚 + 8 𝑛 ?

  • A 6
  • B8
  • C6
  • D4
  • E 4

Q5:

Given that 𝑎 + 2 𝑏 = 7 , what is the value of 3 𝑎 + 6 𝑏 ?

  • A21
  • B10
  • C18
  • D15
  • E24

Q6:

If 3 𝑐 2 𝑏 = 5 and 2 𝑎 + 𝑑 = 3 , what is the value of 6 𝑎 + 3 𝑑 3 𝑐 + 2 𝑏 ?

  • A12
  • B 1 4
  • C14
  • D 4
  • E 1 2

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