Worksheet: Rewriting Expressions Using the Distributive Property

In this worksheet, we will practice rewriting algebraic expressions using the distributive property.

Q1:

Using the distributive property, rewrite the expression (2𝑥8)(6).

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

Q2:

Expand 2𝑥(5𝑥5𝑥).

  • A 1 0 𝑥 + 1 0 𝑥
  • B 3 𝑥 7 𝑥
  • C 1 0 𝑥 + 1 0 𝑥
  • D 1 0 𝑥 1 0 𝑥
  • E 1 0 𝑥 5 𝑥

Q3:

Expand and simplify 4(2𝑥+3)+2(4𝑥+4).

  • A 1 6 𝑥 + 7
  • B 6 𝑥 + 2 0
  • C 1 6 𝑥 + 2 0
  • D 1 2 𝑥 + 7
  • E 1 2 𝑥 + 1 4

Q4:

Use the distributive property to rewrite the algebraic expression 4(𝑥9).

  • A 4 𝑥 3 6
  • B 𝑥 3 6
  • C 3 6 4 𝑥
  • D 4 𝑥 9
  • E 3 6 𝑥

Q5:

Which of the following demonstrates the distributive property?

  • A 4 + ( 𝑥 + 3 ) = 3 + ( 𝑥 4 )
  • B 4 𝑥 + 3 = 3 4 𝑥
  • C 4 ( 𝑥 + 3 ) = 4 𝑥 1 2
  • D 4 𝑥 + 3 + 0 = 4 𝑥 + 3

Q6:

Identify the expression which is not equivalent to the other three.

  • A 9 ( 𝑥 1 7 )
  • B 4 𝑥 1 7 + 5 𝑥
  • C 8 + 9 𝑥 9
  • D 9 𝑥 1 7

Q7:

Benjamin had b dollars in his savings account and then he deposited $11. seven months later, his balance had doubled. Which of the following is equivalent to his new balance of 2(𝑏+11) dollars?

  • A 𝑏 + 2 2
  • B 2 𝑏 + 2 2
  • C 2 𝑏 + 1 1
  • D 𝑏 + 1 3
  • E 2 𝑏 + 1 3

Q8:

Write an expression in terms of 𝑥, for the perimeter of the figure below.

  • A 1 9 𝑥 length units
  • B 3 4 𝑥 length units
  • C 2 3 𝑥 length units
  • D 3 8 𝑥 length units
  • E 6 0 𝑥 length units

Q9:

Find the perimeter of the following shape.

  • A 6 𝑥 + 1 4
  • B 3 𝑥 + 7
  • C 2 𝑥 + 1 0 𝑥 + 1 2
  • D 2 𝑥 + 1 0 𝑥 1 2
  • E 5 𝑥 + 1 1

Q10:

A square of side 3 cm has a square of side 6𝑥 cm cut from one corner as shown in the diagram. Write, in its simplest form, an expression for the perimeter of the remaining shape.

Q11:

Factor 30𝑎𝑏+45𝑎𝑏 completely.

  • A 1 5 𝑎 𝑏 ( 2 𝑏 + 3 𝑎 )
  • B 1 5 𝑎 𝑏 ( 2 𝑏 + 3 𝑎 𝑏 )
  • C 3 0 𝑎 𝑏 ( 2 𝑏 + 4 5 𝑎 𝑏 )
  • D 1 5 𝑎 𝑏 ( 3 0 𝑏 + 3 𝑎 )
  • E 1 5 𝑎 𝑏 ( 2 𝑏 + 4 5 𝑎 𝑏 )

Q12:

A student solving the equation 4(𝑥3)=24 writes down 4𝑥12=24 as their first line of working. What algebraic property did they use?

  • Athe associative property
  • Bthe distributive property
  • Cthe property of opposites
  • Dthe zero property of addition
  • Ethe commutative property

Q13:

Determine the value of 𝑥 that makes the equation 4(7+5)=28+𝑥 true.

Q14:

Use the properties of real numbers to rewrite 6(𝑥+3) as an equivalent expression that does not contain parentheses.

  • A 6 𝑥 + 3
  • B 3 𝑥 + 1 8
  • C 6 𝑥 + 6
  • D 6 𝑥 + 1 8
  • E 6 𝑥 + 9

Q15:

What property is illustrated by the shown step: 𝑥+4𝑥312=0𝑥(𝑥+4)3(𝑥+4)=0?

  • AThe distributive property of multiplication over addition
  • BThe commutative property of addition
  • CThe associative property of addition
  • DThe commutative property of multiplication
  • EThe associative property of multiplication

Q16:

Which of the following expressions is equivalent to 7(38𝑥)?

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

Q17:

Using the diagram, rewrite 𝑑2(𝑒+𝑓) without brackets.

  • A 𝑑 2 𝑒 + 2 𝑓
  • B 𝑑 𝑒 𝑓
  • C 𝑑 2 𝑒 2 𝑓
  • D 𝑑 2 𝑒 𝑓
  • E 𝑑 𝑒 + 𝑓

Q18:

What property is illustrated by the step 𝑥(𝑥+4)3(𝑥+4)=0(𝑥3)(𝑥+4)=0?

  • AThe associative property of multiplication
  • BThe distributive property of multiplication over addition
  • CThe commutative property of multiplication
  • DThe associative property of addition
  • EThe commutative property of addition

Q19:

Use the distributive property to fully expand (𝑥+2)(𝑥+3).

  • A 𝑥 + 5
  • B 𝑥 + 5 𝑥 + 6
  • C 𝑥 + 5 𝑥 + 5
  • D 𝑥 + 6 𝑥 + 5
  • E 𝑥 + 6

Q20:

What property is illustrated by the equation (𝑎+𝑏)𝑥=𝑎𝑥+𝑏𝑥?

  • Athe distributive property of multiplication over addition
  • Bthe associative property of addition
  • Cthe commutative property of addition
  • Dthe commutative property of multiplication
  • Ethe associative property of multiplication

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