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 7𝑎+6𝑏 to 5𝑐+𝑏5𝑎.

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

Q2:

Subtract 19𝑦+18𝑥 from 23𝑥24𝑦.

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

Q3:

Subtract 7𝑦+𝑧3𝑥 from 6𝑥+5𝑧8𝑦.

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

Q4:

Add 38𝑥33𝑦+28𝑧, 24𝑦23𝑥23𝑧, and 24𝑥11𝑧17𝑦, then subtract the result from 26𝑥17𝑦+19𝑧.

  • A 1 3 𝑥 9 𝑦 2 5 𝑧
  • B 5 9 𝑥 2 5 𝑦 3 𝑧
  • C 1 3 𝑥 + 9 𝑦 + 2 5 𝑧
  • D 5 9 𝑥 + 2 5 𝑦 + 3 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 7𝑎𝑏2𝑐𝑑𝑒𝑓 to 8𝑒𝑓9𝑐𝑑5𝑎𝑏.

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

Q7:

Subtract 8𝑥𝑦+2𝑥𝑦+6𝑥𝑦 from 𝑥𝑦8𝑥𝑦+9𝑥𝑦.

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

Q8:

Subtract 6𝑥4𝑦𝑧 from the sum of 9𝑥+8𝑦7𝑧 and 8𝑥9𝑦6𝑧.

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

Q9:

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

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

Q10:

Simplify 𝑡+52𝑡+2.

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

Q11:

Find 𝐴𝐵 given that 𝐴=7𝑝4𝑝+5 and 𝐵=3𝑝4𝑝+1.

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

Q12:

Find 𝐴𝐵 given 𝐴=5𝑥3𝑥 and 𝐵=6𝑥+3𝑥.

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

Q13:

Simplify 2𝑎4𝑎9+5𝑎3𝑎+1.

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

Q14:

Find 𝐴+𝐵 given that 𝐴=7𝑦4𝑦+5 and 𝐵=3𝑦4𝑦+1.

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

Q15:

Simplify 8𝑦3𝑦+23𝑦+5𝑦+1.

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

Q16:

Michael had 3𝑥+6 coins and gave 2𝑥+3 coins to James. How many coins does Michael have left?

  • A 3 𝑥
  • B 3 𝑥 + 6 2 𝑥 + 3
  • C 𝑥 + 3
  • D 5 𝑥 + 9
  • E 𝑥 + 6

Q17:

Simplify (2𝑠+1)(3𝑠+2).

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

Q18:

Simplify (2𝑠+1)+(3𝑠+2).

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

Q19:

Find 𝐴+𝐵 given 𝐴=5𝑠3𝑠 and 𝐵=6𝑠+3𝑠.

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

Q20:

Find 𝐴𝐵 given 𝐴=8𝑥+2 and 𝐵=5𝑥1.

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

Q21:

Simplify 𝑧+5+2𝑧+2.

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

Q22:

Simplify 8𝑥3𝑥+2+3𝑥+5𝑥+1.

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

Q23:

Find 𝐴𝐵 given that 𝐴=3𝑞+5 and 𝐵=2𝑞+6.

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

Q24:

Find 𝐴+𝐵 given 𝐴=3𝑡+5 and 𝐵=2𝑡+6.

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

Q25:

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

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

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