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Worksheet: Factoring the Sum and Difference of Two Cubes

In this worksheet, we will practice factoring the sum and the difference of two cubes.

Q1:

The expression 𝑥 + 2 7 3 has two factors. One factor is ( 𝑥 + 3 ) . What is the other factor?

  • A 𝑥 − 9 𝑥 + 2 7 2
  • B 𝑥 + 3 𝑥 + 9 2
  • C 𝑥 + 3 𝑥 − 9 2
  • D 𝑥 − 3 𝑥 + 9 2
  • E 𝑥 − 3 𝑥 + 2 7 3

Q2:

The expression 𝑥 + 6 4 3 has two factors. One factor is ( 𝑥 + 4 ) . What is the other factor?

  • A 𝑥 − 1 6 𝑥 + 6 4 2
  • B 𝑥 + 4 𝑥 + 1 6 2
  • C 𝑥 + 4 𝑥 − 1 6 2
  • D 𝑥 − 4 𝑥 + 1 6 2
  • E 𝑥 − 4 𝑥 + 6 4 3

Q3:

The expression 𝑥 − 6 4 3 has two factors. One factor is 𝑥 + 4 𝑥 + 1 6 2 . What is the other factor?

  • A ( 𝑥 + 1 6 )
  • B ( 𝑥 + 4 )
  • C ( 𝑥 − 1 6 )
  • D ( 𝑥 − 4 )
  • E 𝑥 + 1 6 2

Q4:

The expression 𝑥 − 2 1 6 3 has two factors. One factor is 𝑥 + 6 𝑥 + 3 6 2 . What is the other factor?

  • A ( 𝑥 + 3 6 )
  • B ( 𝑥 + 6 )
  • C ( 𝑥 − 3 6 )
  • D ( 𝑥 − 6 )
  • E 𝑥 + 3 6 2

Q5:

Given that 𝑥 − 5 1 2 = ( 𝑥 − 8 ) 𝑥 + 𝑘 + 6 4 3 2 , find an expression for 𝑘 .

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

Q6:

Completely factor .

  • A
  • B
  • C
  • D

Q7:

Completely factor .

  • A
  • B
  • C
  • D

Q8:

Completely factor .

  • A
  • B
  • C
  • D

Q9:

Complete the factoring: .

  • A
  • B
  • C
  • D

Q10:

Completely factor .

  • A
  • B
  • C
  • D

Q11:

Completely factor .

  • A
  • B
  • C
  • D

Q12:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q13:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q14:

If 𝑦 + 𝑎 = ( 𝑦 − 3 ) 𝑦 + 3 𝑦 + 9 3 2 , what is the value of 𝑎 ?

Q15:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q16:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q17:

If 𝑥 + 𝑘 = ( 𝑥 + 𝑘 ) 𝑥 − 2 𝑥 + 𝑘 3 3 2 2 , what is the value of 𝑘 ?

Q18:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q19:

If 𝑎 − 𝑏 = 4 5 3 3 and 𝑎 − 𝑏 = 9 , what is the value of 𝑎 + 𝑎 𝑏 + 𝑏 2 2 ?

Q20:

Completely factor .

  • A
  • B
  • C
  • D

Q21:

Complete the following: = ( 𝑦 + 1 5 𝑥 ) 𝑦 − 1 5 𝑦 𝑥 + 2 2 5 𝑥 2 2 .

  • A 𝑦 − 1 5 3
  • B 𝑦 − 2 2 5 3
  • C 𝑦 + 3 3 7 5 3
  • D 𝑦 + 3 3 7 5 𝑥 3 3
  • E 𝑦 + 2 2 5 𝑥 3 3

Q22:

If 𝑥 − 𝑦 = 5 5 2 2 , 𝑥 − 𝑦 = − 5 , and 𝑥 − 𝑥 𝑦 + 𝑦 = 4 9 2 2 , what is the value of 𝑥 + 𝑦 3 3 ?

Q23:

Complete the following: 7 2 9 𝑥 + 8 = ( + ) 8 1 𝑥 − 1 8 𝑥 + 3 2 .

  • A 9 𝑥 4 4 , ,
  • B 9 𝑥 1 8 , ,
  • C 1 8 𝑥 4 4 , ,
  • D 9 𝑥 2 4 , ,
  • E 9 𝑥 4 8 , ,

Q24:

What is the result of 2 7 𝑥 − 1 ÷ ( 3 𝑥 − 1 ) 3 , where 3 𝑥 ≠ 1 ?

  • A 9 𝑥 − 3 𝑥 + 1 2
  • B 9 𝑥 − 3 𝑥 − 1 2
  • C ( 3 𝑥 − 1 ) 2
  • D 9 𝑥 + 3 𝑥 + 1 2
  • E 9 𝑥 + 1 2

Q25:

Completely factor .

  • A
  • B
  • C
  • D
  • E

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