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.

  • A5𝑐+7𝑏+12𝑎
  • B5𝑐+7𝑏+2𝑎
  • C5𝑐+5𝑏+2𝑎
  • D5𝑐+7𝑏+2𝑎

Q2:

Subtract 19𝑦+18𝑥 from 23𝑥24𝑦.

  • A5𝑥+43𝑦
  • B41𝑥5𝑦
  • C4𝑥+42𝑦
  • D5𝑥43𝑦
  • E41𝑥+5𝑦

Q3:

Subtract 7𝑦+𝑧3𝑥 from 6𝑥+5𝑧8𝑦.

  • A9𝑥+6𝑧15𝑦
  • B3𝑥+4𝑧15𝑦
  • C9𝑥+4𝑧15𝑦
  • D9𝑥+4𝑧𝑦

Q4:

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

  • A13𝑥9𝑦25𝑧
  • B59𝑥25𝑦3𝑧
  • C13𝑥+9𝑦+25𝑧
  • D59𝑥+25𝑦+3𝑧
  • E13𝑥+9𝑦+25𝑧

Q5:

Find the area of the shaded region.

  • A45𝑥+30𝑥𝑦75𝑦 cm2
  • B45𝑥+30𝑥𝑦+75𝑦 cm2
  • C45𝑥30𝑥𝑦75𝑦 cm2
  • D45𝑥30𝑥𝑦+75𝑦 cm2

Q6:

Add 7𝑎𝑏2𝑐𝑑𝑒𝑓 to 8𝑒𝑓9𝑐𝑑5𝑎𝑏.

  • A9𝑒𝑓11𝑐𝑑+2𝑎𝑏
  • B7𝑒𝑓11𝑐𝑑+2𝑎𝑏
  • C7𝑒𝑓11𝑐𝑑+12𝑎𝑏
  • D7𝑒𝑓+7𝑐𝑑+2𝑎𝑏

Q7:

Subtract 8𝑥𝑦+2𝑥𝑦+6𝑥𝑦 from 𝑥𝑦8𝑥𝑦+9𝑥𝑦.

  • A𝑥𝑦6𝑥𝑦+5𝑥𝑦
  • B17𝑥𝑦10𝑥𝑦7𝑥𝑦
  • C17𝑥𝑦10𝑥𝑦7𝑥𝑦
  • D𝑥𝑦6𝑥𝑦+5𝑥𝑦

Q8:

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

  • A11𝑥+3𝑦12𝑧
  • B23𝑥5𝑦14𝑧
  • C23𝑥5𝑦14𝑧
  • D11𝑥+3𝑦12𝑧

Q9:

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

  • A21𝑥+127𝑥20
  • B9𝑥+83𝑥20
  • C15𝑥+22𝑥20
  • D6𝑥+105𝑥9
  • E6𝑥+105𝑥20

Q10:

Simplify 𝑡+52𝑡+2.

  • A3𝑡+7
  • B𝑡+7
  • C3𝑡+3
  • D𝑡3
  • E𝑡+3

Q11:

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

  • A4𝑝+4
  • B4𝑝+8𝑝+4
  • C10𝑝+8𝑝+6
  • D10𝑝+4
  • E4𝑝+6

Q12:

Find 𝐴𝐵 given 𝐴=5𝑥3𝑥 and 𝐵=6𝑥+3𝑥.

  • A5𝑥+6𝑥6𝑥
  • B5𝑥+6𝑥3𝑥
  • C11𝑥
  • D5𝑥+6𝑥
  • E11𝑥6𝑥

Q13:

Simplify 2𝑎4𝑎9+5𝑎3𝑎+1.

  • A7𝑎7𝑎3𝑎8
  • B7𝑎4𝑎3𝑎8
  • C7𝑎4𝑎+3𝑎8
  • D7𝑎+4𝑎3𝑎8
  • E7𝑎+4𝑎+3𝑎8

Q14:

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

  • A7𝑦8𝑦+6
  • B2𝑦8𝑦+6
  • C10𝑦+8𝑦+6
  • D10𝑦8𝑦+4
  • E10𝑦8𝑦+6

Q15:

Simplify 8𝑦3𝑦+23𝑦+5𝑦+1.

  • A5𝑦8𝑦+1
  • B11𝑦8𝑦+1
  • C5𝑦+2𝑦+1
  • D5𝑦8𝑦+3
  • E11𝑦+2𝑦+3

Q16:

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

  • A3𝑥
  • B3𝑥+62𝑥+3
  • C𝑥+3
  • D5𝑥+9
  • E𝑥+6

Q17:

Simplify (2𝑠+1)(3𝑠+2).

  • A6𝑠1
  • B5𝑠1
  • C𝑠1
  • D𝑠+3
  • E5𝑠3

Q18:

Simplify (2𝑠+1)+(3𝑠+2).

  • A5𝑠+3
  • B4𝑠+7𝑠+3
  • C6𝑠+3
  • D5𝑠+2
  • E5𝑠3

Q19:

Find 𝐴+𝐵 given 𝐴=5𝑠3𝑠 and 𝐵=6𝑠+3𝑠.

  • A5𝑠+6𝑠
  • B𝑠
  • C5𝑠6𝑠6𝑠
  • D5𝑠
  • E5𝑠6𝑠

Q20:

Find 𝐴𝐵 given 𝐴=8𝑥+2 and 𝐵=5𝑥1.

  • A3𝑥+3
  • B13𝑥+3
  • C3𝑥+1
  • D13𝑥+1
  • E3𝑥+3

Q21:

Simplify 𝑧+5+2𝑧+2.

  • A4𝑧+7
  • B3𝑧+10
  • C3𝑧+7
  • D3𝑧+7
  • E2𝑧+7

Q22:

Simplify 8𝑥3𝑥+2+3𝑥+5𝑥+1.

  • A11𝑥+8𝑥+3
  • B11𝑥+5𝑥+3
  • C24𝑥+2𝑥+3
  • D11𝑥+2𝑥+3
  • E11𝑥+2𝑥1

Q23:

Find 𝐴𝐵 given that 𝐴=3𝑞+5 and 𝐵=2𝑞+6.

  • A𝑞1
  • B5𝑞1
  • C𝑞1
  • D5𝑞+11
  • E𝑞+11

Q24:

Find 𝐴+𝐵 given 𝐴=3𝑡+5 and 𝐵=2𝑡+6.

  • A5𝑡+11
  • B4𝑡+11
  • C16
  • D5𝑡+11
  • E5𝑡+12

Q25:

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

  • A𝑥+71𝑥
  • B𝑥7𝑥+1
  • C𝑥+7𝑥+1
  • D𝑥+1𝑥+7
  • E𝑥+7𝑥1

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