Worksheet: Rewriting Expressions Using the Distributive Property

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

Q1:

Using the distributive property, rewrite the expression ( − 2 𝑥 − 8 ) ( − 6 ) .

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

Q2:

Expand − 2 𝑥 ( 5 𝑥 − 5 𝑥 ) .

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

Q3:

Expand and simplify 4 ( 2 𝑥 + 3 ) + 2 ( 4 𝑥 + 4 ) .

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

Q4:

Use the distributive property to rewrite the algebraic expression 4 ( 𝑥 − 9 ) .

  • A 4 𝑥 − 9
  • B 𝑥 − 3 6
  • C 3 6 − 4 𝑥
  • D 4 𝑥 − 3 6
  • 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 + 0 = − 4 𝑥 + 3
  • D − 4 ( 𝑥 + 3 ) = − 4 𝑥 − 1 2

Q6:

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

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

Q7:

Maged 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 dollars?

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A 3 4 𝑥 length units
  • B 1 9 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 2 𝑥 + 1 0 𝑥 + 1 2 2
  • B 3 𝑥 + 7
  • C 5 𝑥 + 1 1
  • D 6 𝑥 + 1 4
  • E 2 𝑥 + 1 0 𝑥 − 1 2 2

Q10:

A square of side 3 cm has a square of side 6 𝑥 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 3 0 𝑎 𝑏 + 4 5 𝑎 𝑏 2 2 completely.

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

Q12:

A student solving the equation 4 ( 𝑥 − 3 ) = 2 4 writes down 4 𝑥 − 1 2 = 2 4 as their first line of working. What algebraic property did they use?

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

Q13:

Determine the value of 𝑥 that makes the equation 4 ( 7 + 5 ) = 2 8 + 𝑥 true.

Q14:

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

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

Q15:

What property is illustrated by the shown step:

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

Q16:

Which of the following expressions is equivalent to 7 ( 3 − 8 𝑥 ) ?

  • 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

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