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 (−2𝑥−8)(−6).

  • A12𝑥−48
  • B12𝑥−8
  • C−96𝑥
  • D−2𝑥+48
  • E12𝑥+48

Q2:

Expand −2𝑥(5𝑥−5𝑥).

  • A−10𝑥+10𝑥
  • B3𝑥−7𝑥
  • C−10𝑥+10𝑥
  • D−10𝑥−10𝑥
  • E−10𝑥−5𝑥

Q3:

Expand and simplify 4(2𝑥+3)+2(4𝑥+4).

  • A16𝑥+7
  • B6𝑥+20
  • C16𝑥+20
  • D12𝑥+7
  • E12𝑥+14

Q4:

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

  • A4𝑥−36
  • B𝑥−36
  • C36−4𝑥
  • D4𝑥−9
  • E36−𝑥

Q5:

Which of the following demonstrates the distributive property?

  • A−4+(𝑥+3)=3+(𝑥−4)
  • B−4𝑥+3=3−4𝑥
  • C−4(𝑥+3)=−4𝑥−12
  • D−4𝑥+3+0=−4𝑥+3

Q6:

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

  • A9(𝑥−17)
  • B4𝑥−17+5𝑥
  • C−8+9𝑥−9
  • D9𝑥−17

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?

  • A𝑏+22
  • B2𝑏+22
  • C2𝑏+11
  • D𝑏+13
  • E2𝑏+13

Q8:

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

  • A19𝑥 length units
  • B34𝑥 length units
  • C23𝑥 length units
  • D38𝑥 length units
  • E60𝑥 length units

Q9:

Find the perimeter of the following shape.

  • A6𝑥+14
  • B3𝑥+7
  • C2𝑥+10𝑥+12
  • D2𝑥+10𝑥−12
  • E5𝑥+11

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.

  • A15𝑎𝑏(2𝑏+3𝑎)
  • B15𝑎𝑏(2𝑏+3𝑎𝑏)
  • C30𝑎𝑏(2𝑏+45𝑎𝑏)
  • D15𝑎𝑏(30𝑏+3𝑎)
  • E15𝑎𝑏(2𝑏+45𝑎𝑏)

Q12:

A student solving the equation 4(𝑥−3)=24 writes down 4𝑥−12=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.

  • A6𝑥+3
  • B3𝑥+18
  • C6𝑥+6
  • D6𝑥+18
  • E6𝑥+9

Q15:

What property is illustrated by the shown step: 𝑥+4𝑥−3−12=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(3−8𝑥)?

  • A21−56𝑥
  • B21+7𝑥
  • C21−7𝑥
  • D21+56𝑥
  • E56+21𝑥

Q17:

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

  • A𝑑−2𝑒+2𝑓
  • B𝑑−𝑒−𝑓
  • C𝑑−2𝑒−2𝑓
  • D𝑑−2𝑒−𝑓
  • E𝑑−𝑒+𝑓

Q18:

What property is illustrated by the step 𝑥(𝑥+4)−3(𝑥+4)=0(𝑥−3)(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).

  • A𝑥+5
  • B𝑥+5𝑥+6
  • C𝑥+5𝑥+5
  • D𝑥+6𝑥+5
  • E𝑥+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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