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Lesson: Rewriting Expressions Using the Distributive Property

Video

08:25

Sample Question Videos

Worksheet • 16 Questions • 7 Videos

Q1:

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

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

Q2:

Expand βˆ’ 2 π‘₯ ( 5 π‘₯ βˆ’ 5 π‘₯ ) 3 2 .

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

Q3:

Expand and simplify 4 ( 2 π‘₯ + 3 ) + 2 ( 4 π‘₯ + 4 ) .

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

Q4:

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

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

Q5:

Which of the following demonstrates the distributive property?

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

Q6:

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

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

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 π‘₯ , for the perimeter of the figure below.

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

Q9:

Find the perimeter of the following shape.

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

Q10:

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.

Q11:

Factor 3 0 π‘Ž 𝑏 + 4 5 π‘Ž 𝑏 2 2 completely.

  • A 1 5 π‘Ž 𝑏 ( 2 𝑏 + 3 π‘Ž )
  • B 3 0 π‘Ž 𝑏 ( 2 𝑏 + 4 5 π‘Ž 𝑏 )
  • C 1 5 π‘Ž 𝑏 ( 3 0 𝑏 + 3 π‘Ž )
  • D 1 5 π‘Ž 𝑏 ( 2 𝑏 + 3 π‘Ž 𝑏 )
  • E 1 5 π‘Ž 𝑏 ( 2 𝑏 + 4 5 π‘Ž 𝑏 )

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

Q13:

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

Q14:

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

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

Q15:

What property is illustrated by the shown step:

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

Q16:

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

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