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

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In this worksheet, we will practice multiplying the sum of two terms with their difference to get the polynomial known as “the difference of two squares.”

Q1:

Expand the product ( 𝑥 + 1 ) ( 𝑥 − 1 ) .

  • A 𝑥 − 2 𝑥 − 1
  • B 𝑥 + 2 𝑥 − 1
  • C 𝑥 − 1
  • D 𝑥 + 2 𝑥 + 1
  • E 𝑥 + 1

Q2:

Use the difference of two squares identity to expand ( 3 𝑎 + 7 ) ( 3 𝑎 − 7 ) .

  • A 9 𝑎 − 4 9
  • B 9 𝑎 − 4 9
  • C 3 𝑎 − 4 9
  • D 9 𝑎 − 7
  • E 6 𝑎 − 1 4

Q3:

If 𝑥 − 𝑎 = ( 𝑥 + 5 ) ( 𝑥 − 5 ) , what is the value of 𝑎 ?

Q4:

Expand the product ( 2 𝑚 + 𝑛 ) ( 2 𝑚 − 𝑛 ) .

  • A 4 𝑚 + 𝑛
  • B 4 𝑚 + 2 𝑚 𝑛 − 𝑛
  • C 4 𝑚 + 2 𝑚 𝑛 + 𝑛
  • D 4 𝑚 − 2 𝑚 𝑛 + 𝑛
  • E 4 𝑚 − 𝑛

Q5:

If 𝑥 − 𝑦 = 9 and 𝑥 + 𝑦 = 1 0 , what is the value of 𝑥 − 𝑦 ?

Q6:

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

Q7:

If 𝑥 + 𝑦 = 2 and 𝑥 − 𝑦 = 6 , what is the value of 𝑥 − 𝑦 ?

Q8:

If 𝑥 + 𝑙 − 2 5 = ( 𝑥 + 5 ) ( 𝑥 − 5 ) , what is the value of 𝑙 ?

Q9:

Given that 𝑛 + 𝑚 = 5 and 𝑛 − 𝑚 = 4 5 , find 𝑛 − 𝑚 .

Q10:

If 𝑚 − 𝑛 = 6 4 and 𝑚 + 𝑛 = 4 , what is the value of 𝑚 − 𝑛 ?

Q11:

What is the value of √ 7 + √ 3 √ 7 − √ 3 ?

Q12:

Simplify ( 4 𝑧 + 7 ) ( 4 𝑧 − 7 ) .

  • A 1 6 𝑧 − 4 9
  • B 1 6 𝑧 − 5 6 − 4 9
  • C 1 6 𝑧 + 5 6 − 4 9
  • D 1 6 𝑧 + 5 6 + 4 9
  • E 1 6 𝑧 + 4 9

Q13:

Given that 𝑥 = 2 and 𝑦 = √ 3 , find the value of 3 ( 𝑥 + 𝑦 ) ( 𝑥 − 𝑦 ) .

Q14:

Given that 𝑥 − 𝑦 = 6 2 and 𝑥 − 𝑦 = √ 3 1 , find 𝑥 + 𝑦 .

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

Q15:

Given that 𝑥 = 5 √ 7 − √ 2 and 𝑦 = √ 7 − √ 2 , find 𝑥 − 𝑦 expressing your answer in simplest form.

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

Q16:

Expand ( 2 𝑥 − 3 ) ( 2 𝑥 + 3 ) .

  • A 4 𝑥 + 9
  • B − 4 𝑥 − 9
  • C 4 𝑥 − 9
  • D 4 𝑥 + 6 𝑥 − 9
  • E 4 𝑥 + 1 2 𝑥 − 9

Q17:

Simplify √ 3 + 2 √ 3 − 2 .

Q18:

What is the area of a rectangle of length ( 𝑥 + 1 4 ) cm and width ( 𝑥 − 1 4 ) cm?

  • A ( 𝑥 + 1 4 ) cm2
  • B 𝑥 + 1 9 6 cm2
  • C ( 𝑥 − 1 4 ) cm2
  • D 𝑥 − 1 9 6 cm2
  • E 2 𝑥 cm2

Q19:

If 𝑥 − 𝑎 = ( 𝑥 + 1 0 ) ( 𝑥 − 1 0 ) , what is the value of 𝑎 ?

Q20:

If 𝑎 − 𝑏 = 1 0 and 𝑎 + 𝑏 = 1 8 , what is the value of 𝑎 − 𝑏 ?

Q21:

If 𝑚 − 𝑛 = 5 and 𝑚 + 𝑛 = 1 4 , what is the value of 𝑚 − 𝑛 ?

Q22:

If 𝑥 + 𝑦 = 9 and 𝑥 − 𝑦 = 6 , what is the value of 𝑥 − 𝑦 ?

Q23:

Given that 𝑥 + 𝑧 = 3 and 𝑥 − 𝑧 = 3 , find 𝑥 − 𝑧 .

Q24:

If 𝑥 + 𝑙 − 1 4 4 = ( 𝑥 + 1 2 ) ( 𝑥 − 1 2 ) , what is the value of 𝑙 ?

Q25:

Using the difference of two squares, evaluate 2 1 × 1 9 without a calculator.

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