Worksheet: Simplifying Polynomials by Combining Like Terms

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

Q1:

Simplify 7 + ( 2 𝑥 + 1 5 ) .

  • A 1 5 + 9 𝑥
  • B 2 2 + 9 𝑥
  • C 7 + 9 𝑥
  • D 2 2 + 2 𝑥
  • E 1 7 + 2 𝑥

Q2:

Simplify 3 𝑥 − 5 𝑥 + 5 𝑥 + 8 .

  • A − 7 𝑥 + 8
  • B 1 3 𝑥 + 8
  • C − 1 3 𝑥 + 8
  • D 3 𝑥 + 8

Q3:

Simplify the expression 6 𝑥 + 2 𝑦 − 3 𝑥 − 4 𝑦 .

  • A 3 𝑥 + 2 𝑦
  • B 2 𝑥 − 3 𝑦
  • C 8 𝑥 − 7 𝑦
  • D 3 𝑥 − 2 𝑦
  • E 8 𝑥 + 7 𝑦

Q4:

Simplify the expression − 3 𝑥 − 5 𝑥 − 9 𝑥 − 1 1 𝑥 .

  • A − 2 2 𝑥
  • B 2 8 𝑥
  • C − 2 5 𝑥
  • D − 2 8 𝑥
  • E 2 2 𝑥

Q5:

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

  • A 1 1 0 𝑥 − 1 1 2 𝑦
  • B 1 9 2 0 𝑥 + 1 7 1 2 𝑦
  • C 1 5 𝑥 + 5 1 2 𝑦
  • D 1 1 2 0 𝑥 − 1 1 2 𝑦
  • E 1 1 2 0 𝑥 + 1 1 2 𝑦

Q6:

Simplify − 4 𝑥 + 8 𝑦 − 2 𝑧 + 𝑥 − 2 𝑦 − 4 𝑧 4 2 4 2 .

  • A − 5 𝑥 + 1 0 𝑦 + 2 𝑧 4 2
  • B − 3 𝑥 + 6 𝑦 − 6 𝑧 2 8 4
  • C − 5 𝑥 + 1 0 𝑦 + 2 𝑧 2 8 4
  • D − 3 𝑥 + 6 𝑦 − 6 𝑧 4 2

Q7:

The perimeter of a triangle is − 4 𝑥 𝑦 + 9 𝑥 𝑦 − 3 𝑥 𝑦 4 5 2 5 2 c m and the lengths of two of its sides are − 5 𝑥 𝑦 − 6 𝑥 𝑦 4 5 2 c m and 2 𝑥 𝑦 + 4 𝑥 𝑦 2 5 2 c m . Express the length of the third side in terms of 𝑥 and 𝑦 .

  • A − 9 𝑥 𝑦 + 5 𝑥 𝑦 + 𝑥 𝑦 4 5 2 5 2 cm
  • B 𝑥 𝑦 + 1 3 𝑥 𝑦 − 7 𝑥 𝑦 8 1 0 4 2 1 0 4 cm
  • C − 9 𝑥 𝑦 + 5 𝑥 𝑦 + 𝑥 𝑦 8 1 0 4 2 1 0 4 cm
  • D 𝑥 𝑦 + 1 3 𝑥 𝑦 − 7 𝑥 𝑦 4 5 2 5 2 cm

Q8:

Simplify 4 𝑛 + 2 𝑛 𝑚 − 4 𝑚 + 6 𝑛 + 8 𝑛 𝑚 − 3 𝑚 − 1 0 𝑛 𝑚 − 5 𝑛 − 2 𝑚 + 1 2 𝑛 𝑚 + 5 𝑛 − 5 𝑚 2 2 2 2 2 2 2 2 .

  • A − 4 𝑚 + 8 𝑚 𝑛 2
  • B − 1 4 𝑚 + 3 2 𝑚 𝑛 + 1 0 𝑛 2 2
  • C 1 0 𝑚 − 1 2 𝑚 𝑛 − 2 0 𝑛 2 2
  • D − 1 0 𝑚 + 1 2 𝑚 𝑛 + 2 0 𝑛 2 2

Q9:

Add 7 𝑥 𝑦 7 , − 2 𝑦 𝑥 7 , − 9 𝑦 𝑥 7 , and 8 𝑥 𝑦 7 .

  • A 2 2 𝑥 𝑦 7
  • B 4 𝑦 𝑥 7
  • C 2 2 𝑦 𝑥 7
  • D 4 𝑥 𝑦 7

Q10:

Simplify ( 6 𝑥 − 2 𝑧 + 8 𝑦 ) − ( 4 𝑧 − 8 𝑥 + 5 𝑦 ) .

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

Q11:

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

  • A 𝑥 + 4 𝑥 𝑦 − 6 𝑦 2 2
  • B 𝑥 − 3 𝑥 𝑦 − 6 𝑦 2 2
  • C 𝑥 + 7 𝑥 𝑦 − 6 𝑦 2 2
  • D 5 𝑥 − 3 𝑥 𝑦 2
  • E 𝑥 + 7 𝑥 𝑦 2

Q12:

Simplify 1 0 + 𝑥 + 1 1 .

  • A 1 1 + 1 1 𝑥
  • B 2 1 + 1 1 𝑥
  • C 1 0 + 1 1 𝑥
  • D 2 1 + 𝑥
  • E 1 2 + 𝑥

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