Worksheet: Simplifying Expressions: 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+(2𝑥+15).

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

Q2:

Simplify 3𝑥−5𝑥+5𝑥+8.

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

Q3:

Simplify the expression 6𝑥+2𝑦−3𝑥−4𝑦.

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

Q4:

Simplify the expression −3𝑥−5𝑥−9𝑥−11𝑥.

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

Q5:

Simplify the expression 34𝑥+23𝑦−15𝑥−34𝑦.

  • A 1 1 0 𝑥 − 1 1 2 𝑦
  • B 1 5 𝑥 + 5 1 2 𝑦
  • C 1 9 2 0 𝑥 + 1 7 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 −4𝑥+8𝑦−2𝑧+𝑥−2𝑦−4𝑧.

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

Q7:

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

  • A − 9 𝑥 𝑦 + 5 𝑥 𝑦 + 𝑥 𝑦 cm
  • B 𝑥 𝑦 + 1 3 𝑥 𝑦 − 7 𝑥 𝑦 cm
  • C − 9 𝑥 𝑦 + 5 𝑥 𝑦 + 𝑥 𝑦 cm
  • D 𝑥 𝑦 + 1 3 𝑥 𝑦 − 7 𝑥 𝑦 cm

Q8:

Simplify 4𝑛+2𝑛𝑚−4𝑚+6𝑛+8𝑛𝑚−3𝑚−10𝑛𝑚−5𝑛−2𝑚+12𝑛𝑚+5𝑛−5𝑚.

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

Q9:

Add 7𝑥𝑦, −2𝑦𝑥, −9𝑦𝑥, and 8𝑥𝑦.

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

Q10:

Simplify (6𝑥−2𝑧+8𝑦)−(4𝑧−8𝑥+5𝑦).

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

Q11:

Simplify 3𝑥+2𝑥𝑦−3𝑦−5𝑥𝑦−2𝑥−3𝑦.

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

Q12:

Simplify 5+(6𝑥+12).

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

Q13:

Identify like terms, their coefficients, and any constants in the expression −8𝑥−5𝑥+3.

  • Alike terms: −8𝑥, −5𝑥, coefficients: −8, −5, constant: 3
  • Blike terms: 𝑥, 𝑥, coefficients: −8, −5, −5, constant: 𝑥
  • Clike terms: −8𝑥, −5𝑥, coefficients: −8, −5, 3, constant: 3
  • Dlike terms: −8𝑥, −5𝑥, coefficients: −8, −5, 3, constant: 𝑥
  • Elike terms: 𝑥, 𝑥, coefficients: −8, −5, constant: 3

Q14:

Simplify the expression 16𝑥+26𝑥+56𝑥.

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

Q15:

Simplify the expression 111𝑥+310𝑦+711𝑥+110𝑦.

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

Q16:

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

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

Q17:

Which of the following expressions does NOT correspond to the shown diagram?

  • A 𝑚 + 𝑚 + 𝑚 + 𝑚
  • B 4 + 𝑚
  • C 4 ⋅ 𝑚
  • D 4 𝑚
  • E 4 × 𝑚

Q18:

Simplify the expression 38𝑥+58𝑦−14𝑥−14𝑦.

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

Q19:

Simplify 𝑥+𝑥+𝑥+𝑥+𝑥+𝑥+𝑥.

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

Q20:

Simplify the expression 12𝑥−3𝑦−4𝑥−4𝑥+12𝑦−2𝑥+8𝑥.

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

Q21:

Simplify the expression 4𝑥+3𝑥−2𝑥.

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

Q22:

Simplify the expression 311𝑥−−111𝑥+−311𝑥−−111𝑥.

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

Q23:

The algebraic expression 𝑏+5+2𝑏+2 can be interpreted as the number of apples shown in the diagram. The number of apples in each bag is called 𝑏. When rewriting the number of apples in a more natural way (counting all the bags on one hand and all the single apples on the other hand), what properties of addition are we using? Give the new expression for the number of apples.

  • Athe commutative and associative properties, 3𝑏+7
  • Bthe commutative and associative properties, 2𝑏+10
  • Cthe commutative and distributive properties, 3𝑏+7
  • Dthe associative and distributive properties, 3𝑏+10
  • Ethe commutative and distributive properties, 2𝑏+7

Q24:

Simplify the expression 34𝑥+23𝑦+25𝑧−15𝑥−58𝑧+45𝑧−34𝑦.

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

Q25:

Simplify 7×(−1)×𝑏.

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

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