Worksheet: Factoring Quadratics by Combining Like Terms

In this worksheet, we will practice factoring quadratics by collecting like terms.

Q1:

Factorise fully 𝑧 𝑏 𝑧 𝑥 + 𝑏 𝑥 .

  • A ( 𝑥 + 1 ) ( 𝑧 𝑏 )
  • B ( 𝑏 + 1 ) ( 𝑧 𝑥 )
  • C ( 𝑧 1 ) ( 𝑥 𝑏 )
  • D ( 𝑧 + 1 ) ( 𝑏 𝑥 )
  • E ( 𝑥 1 ) ( 𝑏 𝑧 )

Q2:

Factorise fully 4 𝑥 𝑎 + 𝑥 𝑏 + 4 𝑦 𝑎 + 𝑦 𝑏 .

  • A 4 ( 𝑥 + 𝑦 ) ( 𝑎 + 𝑏 )
  • B ( 4 𝑥 + 𝑦 ) ( 𝑎 + 𝑏 )
  • C ( 4 𝑥 + 𝑦 ) ( 4 𝑎 + 𝑏 )
  • D ( 4 𝑎 + 𝑏 ) ( 𝑥 + 𝑦 )

Q3:

Factorise fully 4 𝑥 + 8 𝑥 3 2 5 𝑥 𝑦 + 1 0 𝑦 .

  • A ( 𝑥 2 ) ( 4 𝑥 + 1 6 + 5 𝑦 )
  • B ( 𝑥 + 2 ) ( 4 𝑥 + 1 6 5 𝑦 )
  • C ( 𝑥 2 ) ( 4 𝑥 + 4 5 𝑦 )
  • D ( 𝑥 2 ) ( 4 𝑥 + 1 6 5 𝑦 )
  • E ( 𝑥 2 ) ( 4 𝑥 4 5 𝑦 )

Q4:

Factorise fully 9 𝑥 𝑚 3 𝑥 + 6 𝑚 𝑦 2 𝑥 𝑦 .

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

Q5:

Factorise fully 4 𝑧 𝑥 𝑧 𝑥 + 4 𝑛 𝑧 𝑛 𝑥 .

  • A ( 𝑧 𝑛 + 𝑥 ) ( 4 𝑧 𝑥 )
  • B ( 𝑧 𝑥 𝑛 ) ( 4 𝑧 𝑥 )
  • C ( 𝑧 𝑛 𝑥 ) ( 4 𝑧 + 𝑥 )
  • D ( 𝑧 𝑥 + 𝑛 ) ( 4 𝑧 𝑥 )
  • E ( 𝑧 𝑥 + 𝑛 ) ( 4 𝑥 𝑧 )

Q6:

Factorise fully 𝑥 𝑧 + 1 5 𝑦 𝑢 3 𝑧 𝑦 5 𝑥 𝑢 .

  • A ( 𝑥 3 𝑦 ) ( 𝑢 5 𝑧 )
  • B ( 𝑥 + 3 𝑦 ) ( 𝑧 5 𝑢 )
  • C ( 𝑥 3 𝑦 ) ( 𝑢 + 5 𝑧 )
  • D ( 𝑥 3 𝑦 ) ( 𝑧 5 𝑢 )
  • E ( 𝑦 3 𝑥 ) ( 𝑧 5 𝑢 )

Q7:

Factorise fully 5 𝑧 1 5 𝑦 𝑏 𝑧 + 3 𝑏 𝑦 .

  • A ( 3 𝑦 𝑧 ) ( 𝑏 + 5 )
  • B ( 3 𝑦 + 𝑧 ) ( 𝑏 5 )
  • C ( 3 𝑧 𝑦 ) ( 𝑏 5 )
  • D ( 3 𝑦 𝑧 ) ( 𝑏 5 )
  • E ( 3 𝑧 + 𝑦 ) ( 𝑏 5 )

Q8:

Factorise fully 𝑦 𝑥 + 4 𝑥 + 6 𝑦 + 2 4 .

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

Q9:

Factorise fully 9 𝑥 𝑚 4 𝑙 𝑧 + 4 𝑙 𝑥 9 𝑚 𝑧 .

  • A ( 𝑧 𝑥 ) ( 9 𝑚 + 4 𝑙 )
  • B ( 𝑥 𝑧 ) ( 9 𝑚 4 𝑙 )
  • C ( 𝑧 𝑥 ) ( 9 𝑚 4 𝑙 )
  • D ( 𝑥 𝑧 ) ( 9 𝑚 + 4 𝑙 )
  • E ( 𝑚 𝑙 ) ( 9 𝑥 + 4 𝑧 )

Q10:

Factorise fully 𝑥 𝑦 𝑛 + 𝑦 𝑛 𝑥 𝑛 1 .

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

Q11:

Factorise fully 𝑥 + 1 2 𝑥 𝑦 + 8 𝑥 + 4 8 𝑦 + 3 6 𝑦 .

  • A ( 𝑥 + 6 𝑦 ) ( 𝑥 + 6 𝑦 8 )
  • B ( 𝑥 + 6 𝑦 ) ( 𝑥 6 𝑦 + 8 )
  • C ( 𝑥 + 6 𝑦 8 ) ( 𝑥 + 6 𝑦 + 8 )
  • D ( 𝑥 + 6 𝑦 ) ( 𝑥 + 6 𝑦 + 8 )
  • E 8 ( 𝑥 + 6 𝑦 )

Q12:

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

  • A 53
  • B 14
  • C 34
  • D 33

Q13:

Factorise fully 4 𝑥 + 4 4 𝑥 + 9 6 + 𝑥 𝑦 + 8 𝑦 .

  • A ( 𝑥 + 8 ) ( 4 𝑥 + 1 2 𝑦 )
  • B ( 𝑥 8 ) ( 4 𝑥 + 1 2 + 𝑦 )
  • C ( 𝑥 + 8 ) ( 4 𝑥 + 3 + 𝑦 )
  • D ( 𝑥 + 8 ) ( 4 𝑥 + 1 2 + 𝑦 )
  • E ( 𝑥 + 8 ) ( 4 𝑥 3 + 𝑦 )

Q14:

Factorise fully 2 𝑥 + 2 0 𝑥 + 1 8 7 𝑥 𝑦 6 3 𝑦 .

  • A ( 𝑥 + 9 ) ( 2 𝑥 + 2 + 7 𝑦 )
  • B ( 𝑥 9 ) ( 2 𝑥 + 2 7 𝑦 )
  • C ( 𝑥 + 9 ) ( 2 𝑥 + 1 7 𝑦 )
  • D ( 𝑥 + 9 ) ( 2 𝑥 + 2 7 𝑦 )
  • E ( 𝑥 + 9 ) ( 2 𝑥 1 7 𝑦 )

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