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Lesson: Multiplying the Sum and Difference of the Same Two Terms

Sample Question Videos

Worksheet • 24 Questions • 3 Videos

Q1:

Expand the product ( π‘₯ + 1 ) ( π‘₯ βˆ’ 1 ) .

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

Q2:

Use the difference of two squares identity to expand ( 3 π‘Ž + 7 ) ( 3 π‘Ž βˆ’ 7 ) .

  • A 9 π‘Ž βˆ’ 4 9 2
  • B 9 π‘Ž βˆ’ 4 9
  • C 3 π‘Ž βˆ’ 4 9 2
  • D 6 π‘Ž βˆ’ 1 4 2
  • E 9 π‘Ž βˆ’ 7 2

Q3:

If π‘₯ βˆ’ π‘Ž = ( π‘₯ + 5 ) ( π‘₯ βˆ’ 5 ) 2 , what is the value of π‘Ž ?

Q4:

Expand the product ( 2 π‘š + 𝑛 ) ( 2 π‘š βˆ’ 𝑛 ) .

  • A 4 π‘š βˆ’ 𝑛 2 2
  • B 4 π‘š + 𝑛 2 2
  • C 4 π‘š + 2 π‘š 𝑛 + 𝑛 2 2
  • D 4 π‘š βˆ’ 2 π‘š 𝑛 + 𝑛 2 2
  • E 4 π‘š + 2 π‘š 𝑛 βˆ’ 𝑛 2 2

Q5:

If π‘₯ βˆ’ 𝑦 = 9 and π‘₯ + 𝑦 = 1 0 , what is the value of π‘₯ βˆ’ 𝑦 2 2 ?

Q6:

Complete the following: π‘₯ βˆ’ = ( π‘₯ βˆ’ 5 ) ( π‘₯ + 5 ) 2 .

Q7:

If π‘₯ + 𝑦 = 2 and π‘₯ βˆ’ 𝑦 = 6 , what is the value of π‘₯ βˆ’ 𝑦 2 2 ?

Q8:

If π‘₯ + 𝑙 βˆ’ 2 5 = ( π‘₯ + 5 ) ( π‘₯ βˆ’ 5 ) 2 , what is the value of 𝑙 ?

Q9:

Given that 𝑛 + π‘š = 5 and 𝑛 βˆ’ π‘š = 4 5 2 2 , find 𝑛 βˆ’ π‘š .

Q10:

If π‘š βˆ’ 𝑛 = 6 4 2 2 and π‘š + 𝑛 = 4 , what is the value of π‘š βˆ’ 𝑛 ?

Q11:

What is the value of ο€» √ 7 + √ 3  ο€» √ 7 βˆ’ √ 3  3 3 ?

Q12:

Simplify ( 4 𝑧 + 7 ) ( 4 𝑧 βˆ’ 7 ) .

  • A 1 6 𝑧 βˆ’ 4 9 2
  • B 1 6 𝑧 + 5 6 + 4 9 2
  • C 1 6 𝑧 + 4 9 2
  • D 1 6 𝑧 βˆ’ 5 6 βˆ’ 4 9 2
  • E 1 6 𝑧 + 5 6 βˆ’ 4 9 2

Q13:

Given that π‘₯ = 2 and 𝑦 = √ 3 , find the value of 3 ( π‘₯ + 𝑦 ) ( π‘₯ βˆ’ 𝑦 ) 4 4 .

Q14:

Given that π‘₯ βˆ’ 𝑦 = 6 2 2 2 and π‘₯ βˆ’ 𝑦 = √ 3 1 , find π‘₯ + 𝑦 .

  • A 2 √ 3 1
  • B √ 2
  • C 6 2 √ 3 1
  • D √ 3 1 6 2

Q15:

Given that π‘₯ = 5 √ 7 βˆ’ √ 2 and 𝑦 = √ 7 βˆ’ √ 2 , find π‘₯ βˆ’ 𝑦 2 2 expressing your answer in simplest form.

  • A 4 √ 1 4
  • B 8
  • C 28
  • D 56

Q16:

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

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

Q17:

Simplify ο€» √ 3 + 2  ο€» √ 3 βˆ’ 2  .

Q18:

What is the area of a rectangle of length ( π‘₯ + 1 4 ) cm and width ( π‘₯ βˆ’ 1 4 ) cm?

  • A ο€Ή π‘₯ βˆ’ 1 9 6  2 cm2
  • B 2 π‘₯ cm2
  • C ο€Ή π‘₯ + 1 9 6  2 cm2
  • D ( π‘₯ + 1 4 ) 2 cm2
  • E ( π‘₯ βˆ’ 1 4 ) 2 cm2

Q19:

If π‘₯ βˆ’ π‘Ž = ( π‘₯ + 1 0 ) ( π‘₯ βˆ’ 1 0 ) 2 , what is the value of π‘Ž ?

Q20:

If π‘Ž βˆ’ 𝑏 = 1 0 and π‘Ž + 𝑏 = 1 8 , what is the value of π‘Ž βˆ’ 𝑏 2 2 ?

Q21:

If π‘š βˆ’ 𝑛 = 5 and π‘š + 𝑛 = 1 4 , what is the value of π‘š βˆ’ 𝑛 2 2 ?

Q22:

If π‘₯ + 𝑦 = 9 and π‘₯ βˆ’ 𝑦 = 6 , what is the value of π‘₯ βˆ’ 𝑦 2 2 ?

Q23:

Given that π‘₯ + 𝑧 = 3 and π‘₯ βˆ’ 𝑧 = 3 2 2 , find π‘₯ βˆ’ 𝑧 .

Q24:

If π‘₯ + 𝑙 βˆ’ 1 4 4 = ( π‘₯ + 1 2 ) ( π‘₯ βˆ’ 1 2 ) 2 , what is the value of 𝑙 ?

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