Worksheet: Factoring Difference of Two Squares

In this worksheet, we will practice determining when a quadratic is a difference of two squares and then using this property to factor the expression.

Q1:

Factorise fully 1 0 0 𝑥 1 2 1 𝑦 .

  • A 2 1 ( 𝑥 + 𝑦 ) ( 𝑥 𝑦 )
  • B ( 1 0 𝑥 + 1 1 𝑦 ) ( 1 0 𝑥 1 1 𝑦 )
  • C ( 1 0 𝑥 1 1 𝑦 )
  • D ( 1 1 𝑥 + 1 0 𝑦 ) ( 1 1 𝑥 1 0 𝑦 )
  • E ( 1 1 𝑥 1 0 𝑦 )

Q2:

Factorise fully 9 𝑚 6 4 𝑛 .

  • A 8 𝑚 3 𝑛
  • B 8 𝑚 + 3 𝑛 8 𝑚 3 𝑛
  • C ( 3 𝑚 8 𝑛 )
  • D 1 1 𝑚 + 𝑛 𝑚 𝑛
  • E 3 𝑚 + 8 𝑛 3 𝑚 8 𝑛

Q3:

Factorise fully 1 6 𝑎 𝑏 4 9 .

  • A ( 4 𝑎 𝑏 + 7 ) ( 4 𝑎 𝑏 7 )
  • B 4 𝑎 𝑏 + 7 4 𝑎 𝑏 7
  • C ( 4 𝑎 7 𝑏 )
  • D ( 4 𝑎 𝑏 7 )
  • E ( 4 𝑎 + 7 𝑏 ) ( 4 𝑎 7 𝑏 )

Q4:

Factorise fully 4 9 𝑎 6 4 𝑏 𝑐 .

  • A ( 7 𝑎 8 𝑏 𝑐 )
  • B 4 9 𝑎 + 6 4 𝑏 𝑐 4 9 𝑎 6 4 𝑏 𝑐
  • C ( 7 𝑎 + 8 𝑏 𝑐 ) ( 7 𝑎 8 𝑏 𝑐 )
  • D 7 𝑎 8 𝑏 𝑐
  • E 7 𝑎 + 8 𝑏 𝑐 7 𝑎 8 𝑏 𝑐

Q5:

Find the solution set of 𝑥 1 , 0 8 9 = 0 in .

  • A { 3 3 }
  • B { 3 3 }
  • C { 3 3 , 3 3 }
  • D { 0 , 3 3 }

Q6:

Factorise fully ( 𝑥 + 4 𝑦 + 3 ) ( 𝑥 4 𝑦 3 ) .

  • A ( 4 𝑥 𝑦 3 )
  • B 4 𝑦 ( 4 𝑥 + 3 )
  • C 4 𝑥 ( 4 𝑦 + 3 )
  • D 4 ( 4 𝑦 + 3 𝑥 )
  • E ( 4 𝑥 3 𝑦 )

Q7:

If 𝑥 𝑦 = 8 , what is the value of ( 𝑥 + 3 𝑦 ) ( 𝑥 3 𝑦 ) ?

Q8:

If 𝑥 8 1 𝑦 = 2 4 and 𝑥 + 9 𝑦 = 6 , what is the value of 5 𝑥 4 5 𝑦 ?

Q9:

If 𝑥 1 6 𝑦 = 8 0 and 𝑥 + 4 𝑦 = 5 , what is the value of 4 𝑦 𝑥 ?

Q10:

Factorise fully 4 𝑏 ( 7 𝑎 𝑏 ) 𝑎 ( 7 𝑎 𝑏 ) .

  • A ( 2 𝑎 + 𝑏 ) ( 7 𝑏 𝑎 ) ( 7 𝑏 + 𝑎 )
  • B ( 7 𝑎 𝑏 ) ( 2 𝑏 + 𝑎 ) ( 2 𝑏 𝑎 )
  • C ( 7 𝑏 𝑎 ) ( 2 𝑏 + 𝑎 ) ( 2 𝑏 𝑎 )
  • D ( 7 𝑎 𝑏 ) ( 2 𝑏 𝑎 )
  • E ( 7 𝑎 𝑏 ) ( 4 𝑏 + 𝑎 ) ( 4 𝑏 𝑎 )

Q11:

Factorise fully 𝑥 𝑦 4 9 𝑥 𝑦 .

  • A 𝑥 + 7 𝑦 𝑥 7 𝑦
  • B 𝑥 𝑦 ( 𝑥 + 7 𝑦 ) ( 𝑥 7 𝑦 )
  • C 𝑥 𝑦 𝑥 + 7 𝑦 𝑥 7 𝑦
  • D 𝑥 𝑦 𝑥 + 7 𝑦 𝑥 7 𝑦
  • E 𝑥 𝑦 𝑥 7 𝑦

Q12:

Factorise fully 𝑦 2 5 6 .

  • A ( 𝑦 1 6 )
  • B ( 𝑦 4 ) ( 𝑦 + 4 ) ( 𝑦 1 6 )
  • C ( 𝑦 4 ) ( 𝑦 + 4 ) ( 𝑦 + 1 6 )
  • D ( 𝑦 + 4 ) ( 𝑦 4 )
  • E ( 𝑦 4 ) ( 𝑦 + 4 )

Q13:

By factorising or otherwise, evaluate ( 7 . 4 6 ) ( 2 . 5 4 ) .

Q14:

If 𝑎 + 3 𝑏 = 9 ( 𝑎 3 𝑏 ) = 2 7 , what is the value of 𝑎 9 𝑏 ?

Q15:

Factorise fully 1 6 𝑎 4 9 2 5 𝑏 6 4 .

  • A 1 6 𝑎 4 9 + 2 5 𝑏 6 4 1 6 𝑎 4 9 2 5 𝑏 6 4
  • B 4 𝑎 7 + 5 𝑏 8 4 𝑎 7 5 𝑏 8
  • C 4 𝑎 7 5 𝑏 8
  • D 4 𝑎 7 + 5 𝑏 8 4 𝑎 7 5 𝑏 8
  • E 4 𝑎 4 9 + 5 𝑏 6 4 4 𝑎 4 9 5 𝑏 6 4

Q16:

By considering the difference of two squares, evaluate 9 1 × 8 9 without a calculator.

Q17:

If 𝑥 > 1 0 𝑦 , 𝑥 2 0 𝑥 𝑦 + 1 0 0 𝑦 = 3 6 , and 𝑥 + 1 0 𝑦 = 2 , what is the value of 𝑥 1 0 0 𝑦 ?

Q18:

Factorise fully 9 𝑥 1 2 1 𝑦 𝑧 .

  • A ( 1 1 𝑥 3 𝑦 𝑧 )
  • B ( 3 𝑥 1 1 𝑦 𝑧 )
  • C ( 1 1 𝑥 + 3 𝑦 𝑧 ) ( 1 1 𝑥 3 𝑦 𝑧 )
  • D 1 4 ( 𝑥 + 𝑦 𝑧 ) ( 𝑥 𝑦 𝑧 )
  • E ( 3 𝑥 + 1 1 𝑦 𝑧 ) ( 3 𝑥 1 1 𝑦 𝑧 )

Q19:

If 2 5 𝑥 1 6 𝑦 = 5 𝑥 + 4 𝑦 , what is the value of 5 𝑥 4 𝑦 ?

  • A4
  • B1
  • C25
  • D5

Q20:

By considering the difference of two squares, find the value of 𝑥 for which 3 9 1 9 = 2 0 𝑥 .

Q21:

Factorise fully 6 4 4 9 𝑛 .

  • A ( 8 + 7 𝑛 ) ( 8 7 𝑛 )
  • B ( 7 𝑛 + 8 ) ( 7 𝑛 8 )
  • C ( 8 7 𝑛 )
  • D ( 8 𝑛 + 7 ) ( 8 𝑛 7 )
  • E ( 7 𝑛 8 )

Q22:

Factorise fully 6 2 5 𝑥 1 6 𝑦 .

  • A 2 5 𝑥 + 4 𝑦 2 5 𝑥 4 𝑦
  • B 4 𝑥 + 2 5 𝑦 4 𝑥 2 5 𝑦
  • C 2 5 𝑥 4 𝑦
  • D 3 ( 2 5 𝑥 4 𝑦 )
  • E 2 5 𝑥 + 4 𝑦 2 5 𝑥 4 𝑦

Q23:

Factorise fully and evaluate ( 6 . 8 6 2 ) ( 3 . 1 3 8 ) .

Q24:

Factorise fully 2 𝑚 5 0 𝑚 𝑛 .

  • A 2 ( 5 𝑚 + 𝑛 )
  • B 2 𝑚 ( 5 𝑚 + 𝑛 ) ( 5 𝑚 𝑛 )
  • C 2 ( 𝑚 + 5 𝑛 )
  • D 2 𝑚 ( 𝑚 + 5 𝑛 ) ( 𝑚 5 𝑛 )
  • E ( 𝑚 + 5 𝑛 ) ( 𝑚 5 𝑛 )

Q25:

Factorise fully 3 6 𝑎 ( 3 𝑎 + 7 𝑏 ) .

  • A ( 3 3 𝑎 + 4 3 𝑏 ) ( 3 9 𝑎 + 4 3 𝑏 )
  • B ( 3 𝑎 𝑏 )
  • C ( 3 𝑎 + 1 3 𝑏 ) ( 9 𝑎 + 1 3 𝑏 )
  • D ( 3 𝑎 7 𝑏 ) ( 9 𝑎 + 7 𝑏 )
  • E ( 3 3 𝑎 + 2 9 𝑏 ) ( 3 9 𝑎 + 4 3 𝑏 )

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.