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

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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