Worksheet: Simplifying Algebraic Expressions

In this worksheet, we will practice correctly simplifying algebraic expressions by combining like terms and simplifying expressions containing negative numbers and fractions.

Q1:

Is 9 ( 𝑥 4 ) + 2 ( 𝑥 4 ) = 7 ( 𝑥 4 ) correct?

  • Ano
  • Byes

Q2:

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

  • A 𝑥 𝑦 + 1 0 𝑥 𝑦 5 𝑥 𝑦 2 3 2 5
  • B 5 𝑥 𝑦 + 6 𝑥 𝑦 + 1 1 𝑥 𝑦 4 6 4 2 2 1 0
  • C 𝑥 𝑦 + 1 0 𝑥 𝑦 5 𝑥 𝑦 4 6 4 2 2 1 0
  • D 5 𝑥 𝑦 + 6 𝑥 𝑦 + 1 1 𝑥 𝑦 2 3 2 5

Q3:

Simplify × 9 × 6 3 × 1 4 1 𝑚 𝑚 1 4 𝑚 𝑚 + 8 𝑚 1 8 𝑚 2 1 𝑚 3 .

  • A 7 2 9 2
  • B 3 2 7 2 9
  • C 7 2 9 3 2
  • D 2 7 2 9

Q4:

Simplify 6 × 9 × 6 1 8 × 5 4 𝑛 𝑛 + 2 2 𝑛 .

Q5:

Simplify the expression 1 6 𝑥 + 2 6 𝑥 + 5 6 𝑥 .

  • A 7 6 𝑥
  • B 8 3 𝑥
  • C 3 4 𝑥
  • D 4 3 𝑥
  • E 6 7 𝑥

Q6:

Simplify the expression 1 1 1 𝑥 + 3 1 0 𝑦 + 7 1 1 𝑥 + 1 1 0 𝑦 .

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

Q7:

Simplify the expression 3 𝑥 + ( 2 𝑦 ) ( 3 𝑥 ) + 8 𝑥 ( 4 𝑦 ) + 3 𝑦 ( 2 𝑦 ) .

  • A 8 𝑥 + 7 𝑦
  • B 8 𝑥 5 𝑦
  • C 1 4 𝑥 5 𝑦
  • D 1 4 𝑥 + 7 𝑦
  • E 1 4 𝑥 + 1 1 𝑦

Q8:

Simplify the expression 3 8 𝑥 + 5 8 𝑦 1 4 𝑥 1 4 𝑦 .

  • A 5 8 𝑥 + 7 8 𝑦
  • B 3 8 𝑥 + 1 8 𝑦
  • C 7 8 𝑥 + 5 8 𝑦
  • D 1 8 𝑥 + 3 8 𝑦
  • E 2 8 𝑥 + 4 8 𝑦

Q9:

Simplify 𝑥 + 𝑥 + 𝑥 + 𝑥 + 𝑥 + 𝑥 + 𝑥 .

  • A 7 + 𝑥
  • B 𝑥 7
  • C 6 𝑥
  • D 7 𝑥
  • E 𝑥 6

Q10:

Simplify the expression 1 2 𝑥 3 𝑦 4 𝑥 4 𝑥 + 1 2 𝑦 2 𝑥 + 8 𝑥 2 2 2 .

  • A 4 𝑥 + 9 𝑦 + 6 𝑥 2
  • B 8 𝑥 + 9 𝑦 + 4 𝑥 2
  • C 1 8 𝑥 + 1 5 𝑦 + 1 2 𝑥 2
  • D 6 𝑥 + 9 𝑦 + 4 𝑥 2
  • E 6 𝑥 + 1 5 𝑦 + 1 2 𝑥 2

Q11:

Simplify the expression 4 𝑥 + 3 𝑥 2 𝑥 .

  • A 9 𝑥
  • B 7 𝑥
  • C 3 𝑥
  • D 5 𝑥
  • E 2 𝑥

Q12:

Simplify the expression 3 1 1 𝑥 1 1 1 𝑥 + 3 1 1 𝑥 1 1 1 𝑥 .

  • A 2 1 1 𝑥
  • B 4 1 1 𝑥
  • C 8 1 1 𝑥
  • D 2 1 1 𝑥
  • E 4 1 1 𝑥

Q13:

Simplify the expression 3 4 𝑥 + 2 3 𝑦 + 2 5 𝑧 1 5 𝑥 5 8 𝑧 + 4 5 𝑧 3 4 𝑦 .

  • A 1 1 2 0 𝑥 1 1 2 𝑦 + 7 4 0 𝑧
  • B 1 9 2 0 𝑥 + 1 7 1 2 𝑦 + 7 3 4 0 𝑧
  • C 1 1 2 0 𝑥 + 1 7 1 2 𝑦 + 2 3 4 0 𝑧
  • D 1 1 2 0 𝑥 1 1 2 𝑦 + 2 3 4 0 𝑧
  • E 1 9 2 0 𝑥 1 1 2 𝑦 + 7 3 4 0 𝑧

Q14:

Simplify 7 × ( 1 ) × 𝑏 .

  • A 7 𝑏
  • B 7 𝑏
  • C 𝑏
  • D 7 𝑏
  • E 7 𝑏

Q15:

Simplify the expression 5 9 𝑥 4 9 𝑥 2 9 𝑥 8 9 𝑥 .

  • A 𝑥
  • B 1 9 9 𝑥
  • C 1 4 9 𝑥
  • D 1 9 9 𝑥
  • E 1 4 9 𝑥

Q16:

Simplify the expression 3 𝑥 + ( 2 𝑥 ) ( 3 𝑥 ) + 8 𝑥 .

  • A 1 0 𝑥
  • B 6 𝑥
  • C 1 6 𝑥
  • D 1 2 𝑥
  • E 1 4 𝑥

Q17:

Simplify 1 1 6 𝑏 + 9 2 .

  • A 1 6 𝑏 8 2
  • B 8 1 6 𝑏 2
  • C 1 6 𝑏 + 8 2
  • D 1 6 𝑏 8 2

Q18:

Simplify the expression 1 2 𝑥 3 𝑦 4 𝑥 4 𝑦 + 1 2 𝑧 2 𝑦 + 8 𝑧 .

  • A 9 𝑥 + 4 𝑦 + 6 𝑧
  • B 8 𝑥 7 𝑦 + 2 0 𝑧
  • C 8 𝑥 9 𝑦 + 4 𝑧
  • D 8 𝑥 9 𝑦 + 2 0 𝑧
  • E 9 𝑥 4 𝑦 + 6 𝑧

Q19:

Simplify the expression 3 𝑥 + 3 𝑥 + 9 𝑥 + 7 𝑥 .

  • A 1 5 𝑥
  • B 1 9 𝑥
  • C 2 4 𝑥
  • D 2 2 𝑥
  • E 1 3 𝑥

Q20:

Simplify the expression 2 3 𝑥 3 4 𝑥 5 6 𝑥 4 1 0 𝑥 .

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

Q21:

Simplify the expression 3 1 0 𝑥 4 1 0 𝑥 + 2 1 0 𝑥 1 1 0 𝑥 .

Q22:

Simplify the expression 3 8 𝑥 + 3 4 𝑥 1 2 𝑥 1 8 𝑥 .

  • A 7 4 𝑥
  • B 3 8 𝑥
  • C 1 3 8 𝑥
  • D 1 2 𝑥
  • E 5 8 𝑥

Q23:

Simplify the expression 1 1 0 𝑥 2 5 𝑥 1 2 𝑥 7 1 0 𝑥 .

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

Q24:

Simplify the expression 1 3 𝑥 + 3 5 𝑥 + 9 4 𝑥 + 1 2 𝑥 .

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

Q25:

In the following diagram, 𝑏 is the quantity of water in a full bottle and 𝑔 is that in a full glass. The total quantity of water shown in the diagram can be expressed as 𝑏 + 𝑔 + 𝑔 + 1 2 𝑏 + 3 4 𝑏 . Simplify this expression.

  • A 1 1 4 𝑏 + 3 𝑔
  • B 1 1 4 𝑏 + 2 𝑔
  • C 1 3 4 𝑏 + 2 1 2 𝑔
  • D 2 1 4 𝑏 + 2 𝑔
  • E 2 1 4 𝑏 + 2 1 2 𝑔

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