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Worksheet: Rewriting Expressions

Q1:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q2:

Factor the expression π‘₯ βˆ’ 4 9 2 .

  • A ( π‘₯ βˆ’ 7 ) 2
  • B ( 2 π‘₯ + 7 ) 2
  • C ( 2 π‘₯ βˆ’ 7 ) 2
  • D ( π‘₯ + 7 ) ( π‘₯ βˆ’ 7 )
  • E ( π‘₯ + 4 9 ) ( π‘₯ βˆ’ 4 9 )

Q3:

Factor π‘Ž βˆ’ 6 π‘Ž 𝑏 + 9 𝑏 2 2 .

  • A ( π‘Ž + 𝑏 ) ( π‘Ž + 2 𝑏 )
  • B ( π‘Ž + 3 𝑏 ) 2
  • C ( 2 π‘Ž βˆ’ 𝑏 ) ( π‘Ž βˆ’ 2 𝑏 )
  • D ( π‘Ž βˆ’ 3 𝑏 ) 2
  • E ( π‘Ž + 𝑏 ) ( π‘Ž + 3 𝑏 )

Q4:

Is the equation π‘₯ + 𝑦 π‘₯ + 𝑦 = π‘₯ + 𝑦     an identity?

  • A No
  • B Yes

Q5:

Answer the following questions for the brackets ( π‘₯ βˆ’ 𝑦 ) ( π‘₯ + 𝑦 ) .

Expand the brackets ( π‘₯ βˆ’ 𝑦 ) ( π‘₯ + 𝑦 ) .

  • A π‘₯ + 2 π‘₯ 𝑦 + 𝑦 2 2
  • B π‘₯ + 𝑦 2 2
  • C π‘₯ βˆ’ 2 π‘₯ 𝑦 + 𝑦 2 2
  • D π‘₯ βˆ’ 𝑦 2 2
  • E 𝑦 βˆ’ π‘₯ 2 2

Is the identity ( π‘₯ βˆ’ 𝑦 ) ( π‘₯ + 𝑦 ) = π‘₯ βˆ’ 𝑦 2 2 true?

  • Ayes
  • Bno

Q6:

Factor the expression 4 π‘Ž βˆ’ 9 𝑏 2 2 .

  • A ( 2 π‘Ž βˆ’ 3 𝑏 ) ( 2 π‘Ž βˆ’ 3 𝑏 )
  • B ( 2 π‘Ž + 3 𝑏 ) ( 2 π‘Ž + 3 𝑏 )
  • C ( π‘Ž + 3 𝑏 ) ( 4 π‘Ž βˆ’ 3 𝑏 )
  • D ( 2 π‘Ž + 3 𝑏 ) ( 2 π‘Ž βˆ’ 3 𝑏 )
  • E ( 4 π‘Ž βˆ’ 3 𝑏 ) ( π‘Ž βˆ’ 3 𝑏 )

Q7:

Is the equation π‘₯ + 𝑦 π‘₯ + 𝑦 = π‘₯ + 𝑦 2 2 an identity?

  • A No
  • B Yes

Q8:

Is the equation π‘₯ + 8 π‘₯ + 1 3 = ( π‘₯ + 8 ) βˆ’ 8 π‘₯ βˆ’ 5 1 2 2 an identity?

  • A Yes
  • B No

Q9:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q10:

Expand and simplify ( 2 π‘₯ βˆ’ 3 𝑦 ) ο€Ή 5 π‘₯ βˆ’ 5 π‘₯ 𝑦 βˆ’ 𝑦  2 2 .

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

Q11:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q12:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q13:

Write two equivalent expressions for the area of the following figure.

  • A 1 0 ( π‘₯ + 8 ) , π‘₯ + 8 0
  • B 1 0 ( π‘₯ + 8 ) , 1 0 π‘₯ + 1 8
  • C 2 0 ( π‘₯ + 8 ) , 2 0 π‘₯ + 1 6 0
  • D 1 0 ( π‘₯ + 8 ) , 1 0 π‘₯ + 8 0
  • E 2 0 ( π‘₯ + 8 ) , 2 0 π‘₯ + 2 8

Q14:

An identity is an equation that is true for all values of its variables.

For example, 2 ( π‘Ž + 𝑏 ) = 2 π‘Ž + 2 𝑏 is an identity because it will be true for all values of π‘Ž and 𝑏 .

Expand and simplify ο€Ή π‘₯ βˆ’ 𝑦  + ( 2 π‘₯ 𝑦 ) 2 2 2 2 .

  • A π‘₯ + 2 π‘₯ 𝑦 βˆ’ 𝑦 4 2 2 4
  • B π‘₯ + 4 π‘₯ 𝑦 + 𝑦 4 2 2 4
  • C π‘₯ + 𝑦 4 4
  • D π‘₯ + 2 π‘₯ 𝑦 + 𝑦 4 2 2 4
  • E π‘₯ βˆ’ 𝑦 4 4

Factor π‘₯ + 2 π‘₯ 𝑦 + 𝑦 4 2 2 4 .

  • A ο€Ή π‘₯ + 𝑦  2 2 2
  • B ο€Ή π‘₯ + 𝑦  + 2 π‘₯ 𝑦 2 2 2 2 2
  • C ο€Ή π‘₯ βˆ’ 𝑦  + 2 π‘₯ 𝑦 2 2 2 2 2
  • D ο€Ή π‘₯ βˆ’ 𝑦  2 2 2
  • E ο€Ή π‘₯ βˆ’ 𝑦  βˆ’ 2 π‘₯ 𝑦 2 2 2 2 2

Is the equation ο€Ή π‘₯ + 𝑦  = ο€Ή π‘₯ βˆ’ 𝑦  + ( 2 π‘₯ 𝑦 ) 2 2 2 2 2 2 2 an identity?

  • Ano
  • Byes

Substitute π‘₯ = 3 and 𝑦 = 2 into the identity ( π‘₯ + 𝑦 ) = ( π‘₯ βˆ’ 𝑦 ) + ( 2 π‘₯ 𝑦 ) 2 2 2 2 2 2 2 to generate a Pythagorean triple.

  • A 1 3 = 5 + 1 2 2 2 2
  • B 1 3 = 1 2 βˆ’ 5 2 2 2
  • C 1 3 = ( 5 + 1 2 ) 2 2
  • D 5 = ( 6 βˆ’ 1 ) 2 2
  • E 5 = 3 + 4 2 2 2

Q15:

Factor π‘₯ + 6 π‘₯ + 9 2 .

  • A ( π‘₯ + 3 ) ( 3 π‘₯ + 2 )
  • B ( π‘₯ + 2 ) 2
  • C ( π‘₯ βˆ’ 1 ) ( π‘₯ βˆ’ 9 )
  • D ( π‘₯ + 3 ) 2
  • E ( π‘₯ + 1 ) ( π‘₯ + 9 )

Q16:

Express the following using symbols: The product of 4 and 16 plus 11.

  • A 4 + 1 6 Γ— 1 1
  • B 4 Γ— 1 6 βˆ’ 1 1
  • C 4 βˆ’ 1 6 Γ— 1 1
  • D 4 Γ— 1 6 + 1 1
  • E 4 Γ— 1 1 + 1 6

Q17:

Four friends had a snack together at a cafe. They each ordered a piece of cake for $4.75 and a coffee for $3.50. Which expression represents the total cost of their order?

  • A5($8.25)
  • B4($7.25)
  • C5($7.25)
  • D4($8.25)
  • E4($1.25)