Worksheet: Simplifying Expressions: Combining Like Terms

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 3𝑥5𝑥+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+2𝑦3𝑥4𝑦.

  • 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 3𝑥5𝑥9𝑥11𝑥.

  • 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+23𝑦15𝑥34𝑦.

  • 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+8𝑦2𝑧+𝑥2𝑦4𝑧.

  • 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+9𝑥𝑦3𝑥𝑦cm and the lengths of two of its sides are 5𝑥𝑦6𝑥𝑦cm 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+2𝑛𝑚4𝑚+6𝑛+8𝑛𝑚3𝑚10𝑛𝑚5𝑛2𝑚+12𝑛𝑚+5𝑛5𝑚.

  • 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 (6𝑥2𝑧+8𝑦)(4𝑧8𝑥+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+2𝑥𝑦3𝑦5𝑥𝑦2𝑥3𝑦.

  • 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 8𝑥5𝑥+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+58𝑦14𝑥14𝑦.

  • 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 12𝑥3𝑦4𝑥4𝑥+12𝑦2𝑥+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+3𝑥2𝑥.

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

Q22:

Simplify the expression 311𝑥111𝑥+311𝑥111𝑥.

  • 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+25𝑧15𝑥58𝑧+45𝑧34𝑦.

  • 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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