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Worksheet: Rewriting Expressions Using the Distributive Property

Q1:

Use the distributive property to rewrite the algebraic expression 4 ( π‘₯ βˆ’ 9 ) .

  • A 4 π‘₯ βˆ’ 9
  • B π‘₯ βˆ’ 3 6
  • C 3 6 βˆ’ 4 π‘₯
  • D 4 π‘₯ βˆ’ 3 6
  • E 3 6 βˆ’ π‘₯

Q2:

Using the distributive property, rewrite the expression ( βˆ’ 2 π‘₯ βˆ’ 8 ) ( βˆ’ 6 ) .

  • A 1 2 π‘₯ βˆ’ 8
  • B βˆ’ 9 6 π‘₯
  • C βˆ’ 2 π‘₯ + 4 8
  • D 1 2 π‘₯ + 4 8
  • E 1 2 π‘₯ βˆ’ 4 8

Q3:

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 + 1 1 ) dollars?

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

Q4:

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

Q5:

Using the diagram, rewrite 𝑑 βˆ’ 2 ( 𝑒 + 𝑓 ) without brackets.

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

Q6:

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

  • A 6 π‘₯ + 9
  • B 6 π‘₯ + 3
  • C 6 π‘₯ + 6
  • D 6 π‘₯ + 1 8
  • E 3 π‘₯ + 1 8

Q7:

What property is illustrated by the 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

Q8:

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

Q9:

Find the perimeter of the following shape.

  • A 2 π‘₯ + 1 0 π‘₯ + 1 2 2
  • B 3 π‘₯ + 7
  • C 5 π‘₯ + 1 1
  • D 6 π‘₯ + 1 4
  • E 2 π‘₯ + 1 0 π‘₯ βˆ’ 1 2 2

Q10:

What property is illustrated by the equation ( π‘Ž + 𝑏 ) π‘₯ = π‘Ž π‘₯ + 𝑏 π‘₯ ?

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

Q11:

Write an expression in terms of π‘₯ , for the perimeter of the figure below.

  • A 3 4 π‘₯ length units
  • B 1 9 π‘₯ length units
  • C 2 3 π‘₯ length units
  • D 3 8 π‘₯ length units
  • E 6 0 π‘₯ length units

Q12:

A student solving the equation 4 ( π‘₯ βˆ’ 3 ) = 2 4 writes down 4 π‘₯ βˆ’ 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:

Which of the following demonstrates the distributive property?

  • A βˆ’ 4 + ( π‘₯ + 3 ) = 3 + ( π‘₯ βˆ’ 4 )
  • B βˆ’ 4 π‘₯ + 3 = 3 βˆ’ 4 π‘₯
  • C βˆ’ 4 π‘₯ + 3 + 0 = βˆ’ 4 π‘₯ + 3
  • D βˆ’ 4 ( π‘₯ + 3 ) = βˆ’ 4 π‘₯ βˆ’ 1 2

Q14:

Which of the following expressions is equivalent to 7 ( 3 βˆ’ 8 π‘₯ ) ?

  • A 2 1 + 5 6 π‘₯
  • B 2 1 βˆ’ 7 π‘₯
  • C 2 1 + 7 π‘₯
  • D 2 1 βˆ’ 5 6 π‘₯
  • E 5 6 + 2 1 π‘₯

Q15:

Determine the value of π‘₯ that makes the equation 4 ( 7 + 5 ) = 2 8 + π‘₯ true.

Q16:

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

  • A βˆ’ 8 + 9 π‘₯ βˆ’ 9
  • B 4 π‘₯ βˆ’ 1 7 + 5 π‘₯
  • C 9 π‘₯ βˆ’ 1 7
  • D 9 ( π‘₯ βˆ’ 1 7 )