Worksheet: Addition and Subtraction of Algebraic Expressions

In this worksheet, we will practice adding and subtracting algebraic expressions by adding and subtracting like terms.

Q1:

Add 7 𝑎 + 6 𝑏 2 to 5 𝑐 + 𝑏 5 𝑎 3 2 .

  • A 5 𝑐 + 5 𝑏 + 2 𝑎 3 2
  • B 5 𝑐 + 7 𝑏 + 2 𝑎 3 2
  • C 5 𝑐 + 7 𝑏 + 1 2 𝑎 3 2
  • D 5 𝑐 + 7 𝑏 + 2 𝑎 3 2

Q2:

Subtract 1 9 𝑦 + 1 8 𝑥 from 2 3 𝑥 2 4 𝑦 .

  • A 4 1 𝑥 5 𝑦
  • B 5 𝑥 + 4 3 𝑦
  • C 4 1 𝑥 + 5 𝑦
  • D 5 𝑥 4 3 𝑦
  • E 4 𝑥 + 4 2 𝑦

Q3:

Subtract 7 𝑦 + 𝑧 3 𝑥 from 6 𝑥 + 5 𝑧 8 𝑦 .

  • A 9 𝑥 + 6 𝑧 1 5 𝑦
  • B 9 𝑥 + 4 𝑧 𝑦
  • C 3 𝑥 + 4 𝑧 1 5 𝑦
  • D 9 𝑥 + 4 𝑧 1 5 𝑦

Q4:

Add 3 8 𝑥 3 3 𝑦 + 2 8 𝑧 , 2 4 𝑦 2 3 𝑥 2 3 𝑧 , and 2 4 𝑥 1 1 𝑧 1 7 𝑦 , then subtract the result from 2 6 𝑥 1 7 𝑦 + 1 9 𝑧 .

  • A 5 9 𝑥 2 5 𝑦 3 𝑧
  • B 1 3 𝑥 + 9 𝑦 + 2 5 𝑧
  • C 5 9 𝑥 + 2 5 𝑦 + 3 𝑧
  • D 1 3 𝑥 + 9 𝑦 + 2 5 𝑧
  • E 1 3 𝑥 9 𝑦 2 5 𝑧

Q5:

Find the area of the shaded region.

  • A 4 5 𝑥 + 3 0 𝑥 𝑦 + 7 5 𝑦 cm2
  • B 4 5 𝑥 3 0 𝑥 𝑦 + 7 5 𝑦 cm2
  • C 4 5 𝑥 3 0 𝑥 𝑦 7 5 𝑦 cm2
  • D 4 5 𝑥 + 3 0 𝑥 𝑦 7 5 𝑦 cm2

Q6:

Add 7 𝑎 𝑏 2 𝑐 𝑑 𝑒 𝑓 2 2 3 2 to 8 𝑒 𝑓 9 𝑐 𝑑 5 𝑎 𝑏 3 2 2 2 .

  • A 7 𝑒 𝑓 + 7 𝑐 𝑑 + 2 𝑎 𝑏 3 2 2 2
  • B 9 𝑒 𝑓 1 1 𝑐 𝑑 + 2 𝑎 𝑏 3 2 2 2
  • C 7 𝑒 𝑓 1 1 𝑐 𝑑 + 1 2 𝑎 𝑏 3 2 2 2
  • D 7 𝑒 𝑓 1 1 𝑐 𝑑 + 2 𝑎 𝑏 3 2 2 2

Q7:

Subtract 8 𝑥 𝑦 + 2 𝑥 𝑦 + 6 𝑥 𝑦 from 𝑥 𝑦 8 𝑥 𝑦 + 9 𝑥 𝑦 .

  • A 𝑥 𝑦 6 𝑥 𝑦 + 5 𝑥 𝑦
  • B 1 7 𝑥 𝑦 1 0 𝑥 𝑦 7 𝑥 𝑦
  • C 𝑥 𝑦 6 𝑥 𝑦 + 5 𝑥 𝑦
  • D 1 7 𝑥 𝑦 1 0 𝑥 𝑦 7 𝑥 𝑦

Q8:

Subtract 6 𝑥 4 𝑦 𝑧 3 2 from the sum of 9 𝑥 + 8 𝑦 7 𝑧 3 2 and 8 𝑥 9 𝑦 6 𝑧 3 2 .

  • A 2 3 𝑥 5 𝑦 1 4 𝑧 3 2
  • B 1 1 𝑥 + 3 𝑦 1 2 𝑧 6 4 2
  • C 2 3 𝑥 5 𝑦 1 4 𝑧 6 4 2
  • D 1 1 𝑥 + 3 𝑦 1 2 𝑧 3 2

Q9:

Find an expression for the difference between the areas of the two figures below.

  • A 1 5 𝑥 + 2 2 𝑥 2 0 2
  • B 6 𝑥 + 1 0 5 𝑥 2 0 2
  • C 2 1 𝑥 + 1 2 7 𝑥 2 0 2
  • D 9 𝑥 + 8 3 𝑥 2 0 2
  • E 6 𝑥 + 1 0 5 𝑥 9 2

Q10:

Simplify 𝑡 + 5 2 𝑡 + 2 2 2 .

  • A 𝑡 + 7 2
  • B 3 𝑡 + 3 2
  • C 3 𝑡 + 7 2
  • D 𝑡 + 3 2
  • E 𝑡 3 2

Q11:

Find 𝐴 𝐵 given that 𝐴 = 7 𝑝 4 𝑝 + 5 2 and 𝐵 = 3 𝑝 4 𝑝 + 1 2 .

  • A 1 0 𝑝 + 4 2
  • B 1 0 𝑝 + 8 𝑝 + 6 2
  • C 4 𝑝 + 8 𝑝 + 4 2
  • D 4 𝑝 + 4 2
  • E 4 𝑝 + 6 2

Q12:

Find 𝐴 𝐵 given 𝐴 = 5 𝑥 3 𝑥 3 and 𝐵 = 6 𝑥 + 3 𝑥 2 .

  • A 5 𝑥 + 6 𝑥 3 𝑥 3 2
  • B 1 1 𝑥 3
  • C 1 1 𝑥 6 𝑥 3
  • D 5 𝑥 + 6 𝑥 6 𝑥 3 2
  • E 5 𝑥 + 6 𝑥 3 2

Q13:

Simplify 2 𝑎 4 𝑎 9 + 5 𝑎 3 𝑎 + 1 3 2 3 .

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

Q14:

Find 𝐴 + 𝐵 given that 𝐴 = 7 𝑦 4 𝑦 + 5 2 and 𝐵 = 3 𝑦 4 𝑦 + 1 2 .

  • A 7 𝑦 8 𝑦 + 6 2
  • B 2 𝑦 8 𝑦 + 6 2
  • C 1 0 𝑦 + 8 𝑦 + 6 2
  • D 1 0 𝑦 8 𝑦 + 6 2
  • E 1 0 𝑦 8 𝑦 + 4 2

Q15:

Simplify 8 𝑦 3 𝑦 + 2 3 𝑦 + 5 𝑦 + 1 .

  • A 5 𝑦 + 2 𝑦 + 1
  • B 1 1 𝑦 8 𝑦 + 1
  • C 5 𝑦 8 𝑦 + 3
  • D 5 𝑦 8 𝑦 + 1
  • E 1 1 𝑦 + 2 𝑦 + 3

Q16:

Fady had coins and gave coins to Ramy. How many coins does Fady have left?

  • A
  • B
  • C
  • D
  • E

Q17:

Simplify ( 2 𝑠 + 1 ) ( 3 𝑠 + 2 ) .

  • A 𝑠 + 3
  • B 5 𝑠 3
  • C 5 𝑠 1
  • D 𝑠 1
  • E 6 𝑠 1

Q18:

Simplify ( 2 𝑠 + 1 ) + ( 3 𝑠 + 2 ) .

  • A 4 𝑠 + 7 𝑠 + 3 2
  • B 5 𝑠 3
  • C 6 𝑠 + 3
  • D 5 𝑠 + 3
  • E 5 𝑠 + 2

Q19:

Find 𝐴 + 𝐵 given 𝐴 = 5 𝑠 3 𝑠 3 and 𝐵 = 6 𝑠 + 3 𝑠 2 .

  • A 5 𝑠 6 𝑠 6 𝑠 3 2
  • B 𝑠 3
  • C 5 𝑠 + 6 𝑠 3 2
  • D 5 𝑠 6 𝑠 3 2
  • E 5 𝑠 3

Q20:

Find 𝐴 𝐵 given 𝐴 = 8 𝑥 + 2 and 𝐵 = 5 𝑥 1 .

  • A 3 𝑥 + 1
  • B 1 3 𝑥 + 1
  • C 1 3 𝑥 + 3
  • D 3 𝑥 + 3
  • E 3 𝑥 + 3

Q21:

Simplify 𝑧 + 5 + 2 𝑧 + 2 2 2 .

  • A 3 𝑧 + 1 0 2
  • B 4 𝑧 + 7 2
  • C 2 𝑧 + 7 2
  • D 3 𝑧 + 7 2
  • E 3 𝑧 + 7 4

Q22:

Simplify 8 𝑥 3 𝑥 + 2 + 3 𝑥 + 5 𝑥 + 1 2 2 .

  • A 1 1 𝑥 + 2 𝑥 1 2
  • B 1 1 𝑥 + 8 𝑥 + 3 2
  • C 2 4 𝑥 + 2 𝑥 + 3 2
  • D 1 1 𝑥 + 2 𝑥 + 3 2
  • E 1 1 𝑥 + 5 𝑥 + 3 2

Q23:

Find 𝐴 𝐵 given that 𝐴 = 3 𝑞 + 5 2 and 𝐵 = 2 𝑞 + 6 2 .

  • A 5 𝑞 1 2
  • B 5 𝑞 + 1 1 2
  • C 𝑞 + 1 1 2
  • D 𝑞 1 2
  • E 𝑞 1 2

Q24:

Find 𝐴 + 𝐵 given 𝐴 = 3 𝑡 + 5 2 and 𝐵 = 2 𝑡 + 6 2 .

  • A 5 𝑡 + 1 2 2
  • B 4 𝑡 + 1 1 2
  • C16
  • D 5 𝑡 + 1 1 2
  • E 5 𝑡 + 1 1

Q25:

What is the additive inverse of the algebraic fraction 𝑥 + 7 𝑥 + 1 ?

  • A 𝑥 7 𝑥 + 1
  • B 𝑥 + 1 𝑥 + 7
  • C 𝑥 + 7 𝑥 1
  • D 𝑥 + 7 𝑥 + 1
  • E 𝑥 + 7 1 𝑥

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