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Worksheet: Simplifying Polynomials by Combining Like Terms

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

Q1:

Simplify 1 0 + π‘₯ + 1 1 .

  • A 1 1 + 1 1 π‘₯
  • B 2 1 + 1 1 π‘₯
  • C 1 0 + 1 1 π‘₯
  • D 2 1 + π‘₯
  • E 1 2 + π‘₯

Q2:

Simplify 7 + ( 2 π‘₯ + 1 5 ) .

  • A 1 5 + 9 π‘₯
  • B 2 2 + 9 π‘₯
  • C 7 + 9 π‘₯
  • D 2 2 + 2 π‘₯
  • E 1 7 + 2 π‘₯

Q3:

Simplify 3 π‘₯ βˆ’ 5 π‘₯ + 5 π‘₯ + 8 .

  • A βˆ’ 7 π‘₯ + 8
  • B 1 3 π‘₯ + 8
  • C βˆ’ 1 3 π‘₯ + 8
  • D 3 π‘₯ + 8

Q4:

Simplify βˆ’ 3 π‘₯ βˆ’ 8 π‘₯ + 6 π‘₯ + 1 .

  • A 5 π‘₯ + 1
  • B 1 7 π‘₯ + 1
  • C βˆ’ 1 1 π‘₯ + 1
  • D βˆ’ 5 π‘₯ + 1
  • E βˆ’ 1 7 π‘₯ + 1

Q5:

Simplify the expression 6 π‘₯ + 2 𝑦 βˆ’ 3 π‘₯ βˆ’ 4 𝑦 .

  • A 3 π‘₯ + 2 𝑦
  • B 2 π‘₯ βˆ’ 3 𝑦
  • C 8 π‘₯ βˆ’ 7 𝑦
  • D 3 π‘₯ βˆ’ 2 𝑦
  • E 8 π‘₯ + 7 𝑦

Q6:

Simplify the expression βˆ’ 3 π‘₯ βˆ’ 5 π‘₯ βˆ’ 9 π‘₯ βˆ’ 1 1 π‘₯ .

  • A βˆ’ 2 2 π‘₯
  • B 2 8 π‘₯
  • C βˆ’ 2 5 π‘₯
  • D βˆ’ 2 8 π‘₯
  • E 2 2 π‘₯

Q7:

Simplify βˆ’ 4 π‘₯ + 8 𝑦 βˆ’ 2 𝑧 + π‘₯ βˆ’ 2 𝑦 βˆ’ 4 𝑧 4 2 4 2 .

  • A βˆ’ 5 π‘₯ + 1 0 𝑦 + 2 𝑧 4 2
  • B βˆ’ 3 π‘₯ + 6 𝑦 βˆ’ 6 𝑧 2 8 4
  • C βˆ’ 5 π‘₯ + 1 0 𝑦 + 2 𝑧 2 8 4
  • D βˆ’ 3 π‘₯ + 6 𝑦 βˆ’ 6 𝑧 4 2

Q8:

Simplify βˆ’ 2 𝑦 βˆ’ 4 𝑧 βˆ’ 8 π‘₯ βˆ’ 8 𝑦 βˆ’ 4 𝑧 2 2 .

  • A 8 π‘₯ + 6 𝑦 2
  • B βˆ’ 8 π‘₯ βˆ’ 1 0 𝑦 βˆ’ 8 𝑧 2 4 2
  • C 8 π‘₯ + 6 𝑦 2 4
  • D βˆ’ 8 π‘₯ βˆ’ 1 0 𝑦 βˆ’ 8 𝑧 2

Q9:

The perimeter of a triangle is ο€Ή βˆ’ 4 π‘₯ 𝑦 + 9 π‘₯ 𝑦 βˆ’ 3 π‘₯ 𝑦  4 5 2 5 2 c m and the lengths of two of its sides are ο€Ή βˆ’ 5 π‘₯ 𝑦 βˆ’ 6 π‘₯ 𝑦  4 5 2 c m and ο€Ή 2 π‘₯ 𝑦 + 4 π‘₯ 𝑦  2 5 2 c m . Express the length of the third side in terms of π‘₯ and 𝑦 .

  • A βˆ’ 9 π‘₯ 𝑦 + 5 π‘₯ 𝑦 + π‘₯ 𝑦 4 5 2 5 2 cm
  • B π‘₯ 𝑦 + 1 3 π‘₯ 𝑦 βˆ’ 7 π‘₯ 𝑦 8 1 0 4 2 1 0 4 cm
  • C βˆ’ 9 π‘₯ 𝑦 + 5 π‘₯ 𝑦 + π‘₯ 𝑦 8 1 0 4 2 1 0 4 cm
  • D π‘₯ 𝑦 + 1 3 π‘₯ 𝑦 βˆ’ 7 π‘₯ 𝑦 4 5 2 5 2 cm

Q10:

Simplify ο€Ή 4 𝑛 + 2 𝑛 π‘š βˆ’ 4 π‘š  + ο€Ή 6 𝑛 + 8 𝑛 π‘š βˆ’ 3 π‘š  βˆ’ ο€Ή 1 0 𝑛 π‘š βˆ’ 5 𝑛 βˆ’ 2 π‘š  + ο€Ή 1 2 𝑛 π‘š + 5 𝑛 βˆ’ 5 π‘š  2 2 2 2 2 2 2 2 .

  • A βˆ’ 4 π‘š + 8 π‘š 𝑛 2
  • B βˆ’ 1 4 π‘š + 3 2 π‘š 𝑛 + 1 0 𝑛 2 2
  • C 1 0 π‘š βˆ’ 1 2 π‘š 𝑛 βˆ’ 2 0 𝑛 2 2
  • D βˆ’ 1 0 π‘š + 1 2 π‘š 𝑛 + 2 0 𝑛 2 2

Q11:

Add 7 π‘₯ 𝑦 7 , βˆ’ 2 𝑦 π‘₯ 7 , βˆ’ 9 𝑦 π‘₯ 7 , and 8 π‘₯ 𝑦 7 .

  • A 2 2 π‘₯ 𝑦 7
  • B 4 𝑦 π‘₯ 7
  • C 2 2 𝑦 π‘₯ 7
  • D 4 π‘₯ 𝑦 7

Q12:

Simplify the expression 3 4 π‘₯ + 2 3 𝑦 βˆ’ 1 5 π‘₯ βˆ’ 3 4 𝑦 .

  • A 1 1 0 π‘₯ βˆ’ 1 1 2 𝑦
  • B 1 9 2 0 π‘₯ + 1 7 1 2 𝑦
  • C 1 5 π‘₯ + 5 1 2 𝑦
  • D 1 1 2 0 π‘₯ βˆ’ 1 1 2 𝑦
  • E 1 1 2 0 π‘₯ + 1 1 2 𝑦

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