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).

  • A17+2𝑥
  • B7+9𝑥
  • C22+2𝑥
  • D15+9𝑥
  • E22+9𝑥

Q2:

Simplify 3𝑥5𝑥+5𝑥+8.

  • A13𝑥+8
  • B3𝑥+8
  • C7𝑥+8
  • D13𝑥+8

Q3:

Simplify the expression 6𝑥+2𝑦3𝑥4𝑦.

  • A2𝑥3𝑦
  • B3𝑥2𝑦
  • C8𝑥7𝑦
  • D3𝑥+2𝑦
  • E8𝑥+7𝑦

Q4:

Simplify the expression 3𝑥5𝑥9𝑥11𝑥.

  • A22𝑥
  • B28𝑥
  • C25𝑥
  • D28𝑥
  • E22𝑥

Q5:

Simplify the expression 34𝑥+23𝑦15𝑥34𝑦.

  • A110𝑥112𝑦
  • B15𝑥+512𝑦
  • C1920𝑥+1712𝑦
  • D1120𝑥112𝑦
  • E1120𝑥+112𝑦

Q6:

Simplify 4𝑥+8𝑦2𝑧+𝑥2𝑦4𝑧.

  • A3𝑥+6𝑦6𝑧
  • B3𝑥+6𝑦6𝑧
  • C5𝑥+10𝑦+2𝑧
  • D5𝑥+10𝑦+2𝑧

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.

  • A9𝑥𝑦+5𝑥𝑦+𝑥𝑦 cm
  • B𝑥𝑦+13𝑥𝑦7𝑥𝑦 cm
  • C9𝑥𝑦+5𝑥𝑦+𝑥𝑦 cm
  • D𝑥𝑦+13𝑥𝑦7𝑥𝑦 cm

Q8:

Simplify 4𝑛+2𝑛𝑚4𝑚+6𝑛+8𝑛𝑚3𝑚10𝑛𝑚5𝑛2𝑚+12𝑛𝑚+5𝑛5𝑚.

  • A14𝑚+32𝑚𝑛+10𝑛
  • B10𝑚+12𝑚𝑛+20𝑛
  • C4𝑚+8𝑚𝑛
  • D10𝑚12𝑚𝑛20𝑛

Q9:

Add 7𝑥𝑦, 2𝑦𝑥, 9𝑦𝑥, and 8𝑥𝑦.

  • A22𝑦𝑥
  • B4𝑦𝑥
  • C22𝑥𝑦
  • D4𝑥𝑦

Q10:

Simplify (6𝑥2𝑧+8𝑦)(4𝑧8𝑥+5𝑦).

  • A14𝑥+13𝑦6𝑧
  • B2𝑥+13𝑦+2𝑧
  • C14𝑥+3𝑦6𝑧
  • D14𝑥3𝑦6𝑧
  • E2𝑥+13𝑦6𝑧

Q11:

Simplify 3𝑥+2𝑥𝑦3𝑦5𝑥𝑦2𝑥3𝑦.

  • A5𝑥3𝑥𝑦
  • B𝑥+7𝑥𝑦
  • C𝑥+4𝑥𝑦6𝑦
  • D𝑥3𝑥𝑦6𝑦
  • E𝑥+7𝑥𝑦6𝑦

Q12:

Simplify 5+(6𝑥+12).

  • A18+6𝑥
  • B5+11𝑥
  • C17+6𝑥
  • D12+11𝑥
  • E17+11𝑥

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.

  • A67𝑥
  • B76𝑥
  • C34𝑥
  • D43𝑥
  • E83𝑥

Q15:

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

  • A611𝑥+210𝑦
  • B811𝑥+410𝑦
  • C210𝑥+611𝑦
  • D410𝑥+811𝑦
  • E411𝑥+810𝑦

Q16:

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

  • A14𝑥5𝑦
  • B8𝑥5𝑦
  • C14𝑥+11𝑦
  • D8𝑥+7𝑦
  • E14𝑥+7𝑦

Q17:

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

  • A𝑚+𝑚+𝑚+𝑚
  • B4+𝑚
  • C4𝑚
  • D4𝑚
  • E4×𝑚

Q18:

Simplify the expression 38𝑥+58𝑦14𝑥14𝑦.

  • A58𝑥+78𝑦
  • B28𝑥+48𝑦
  • C18𝑥+38𝑦
  • D78𝑥+58𝑦
  • E38𝑥+18𝑦

Q19:

Simplify 𝑥+𝑥+𝑥+𝑥+𝑥+𝑥+𝑥.

  • A6𝑥
  • B𝑥
  • C7𝑥
  • D𝑥
  • E7+𝑥

Q20:

Simplify the expression 12𝑥3𝑦4𝑥4𝑥+12𝑦2𝑥+8𝑥.

  • A8𝑥+9𝑦+4𝑥
  • B18𝑥+15𝑦+12𝑥
  • C4𝑥+9𝑦+6𝑥
  • D6𝑥+9𝑦+4𝑥
  • E6𝑥+15𝑦+12𝑥

Q21:

Simplify the expression 4𝑥+3𝑥2𝑥.

  • A5𝑥
  • B9𝑥
  • C2𝑥
  • D3𝑥
  • E7𝑥

Q22:

Simplify the expression 311𝑥111𝑥+311𝑥111𝑥.

  • A411𝑥
  • B211𝑥
  • C211𝑥
  • D411𝑥
  • E811𝑥

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.

  • A1920𝑥112𝑦+7340𝑧
  • B1120𝑥112𝑦+2340𝑧
  • C1120𝑥112𝑦+740𝑧
  • D1120𝑥+1712𝑦+2340𝑧
  • E1920𝑥+1712𝑦+7340𝑧

Q25:

Simplify 7×(1)×𝑏.

  • A7𝑏
  • B𝑏
  • C7𝑏
  • D7𝑏
  • E7𝑏

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