Worksheet: Factoring by Grouping

In this worksheet, we will practice factoring expressions by grouping.

Q1:

Factorise fully 𝑥+𝑥130.

  • A ( 𝑥 + 5 ) 𝑥 + 5 𝑥 + 2 6
  • B ( 𝑥 5 ) 𝑥 + 5 𝑥 + 2 6
  • C ( 𝑥 5 ) 𝑥 5 𝑥 + 2 6
  • D ( 𝑥 5 ) 𝑥 + 5 𝑥 + 2 5

Q2:

Factorise fully 𝑥2𝑥+5𝑥10.

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

Q3:

Factorise fully 𝑥+9𝑥8𝑥72.

  • A ( 𝑥 8 ) 𝑥 + 9
  • B 𝑥 8 𝑥 9
  • C 𝑥 8 𝑥 + 9
  • D 𝑥 + 8 𝑥 + 9

Q4:

Factorise fully 𝑧+6𝑧+6+𝑧.

  • A ( 𝑧 + 1 ) 𝑧 + 6
  • B 𝑧 + 1 𝑧 + 6
  • C ( 𝑧 1 ) ( 𝑧 + 1 ) ( 𝑧 + 6 )
  • D 𝑧 + 1 ( 𝑧 + 6 )
  • E ( 𝑧 1 ) 𝑧 + 6

Q5:

Factorise fully 𝑥𝑦27𝑥𝑦+27.

  • A ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 3 ) 𝑦 + 3 𝑦 + 9
  • B ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 3 ) 𝑦 3 𝑦 + 9
  • C ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑦 3
  • D ( 𝑥 1 ) ( 𝑥 + 1 ) 𝑦 + 3
  • E ( 𝑥 1 ) ( 𝑥 + 1 ) ( 𝑦 + 3 ) 𝑦 3 𝑦 + 9

Q6:

Expand 𝑎(𝑎16𝑏)+64𝑏81, and then factorise the result completely.

  • A ( 𝑎 + 8 𝑏 + 9 ) ( 𝑎 + 8 𝑏 9 )
  • B ( 𝑎 + 9 𝑏 ) ( 𝑎 9 𝑏 )
  • C ( 𝑎 8 𝑏 9 )
  • D ( 𝑎 8 𝑏 + 9 ) ( 𝑎 + 8 𝑏 9 )
  • E ( 𝑎 8 𝑏 + 9 ) ( 𝑎 8 𝑏 9 )

Q7:

Factorise fully 𝑥𝑥𝑥+1.

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

Q8:

Expand and simplify 𝑎9𝑏+𝑎𝑏(𝑎9𝑏), then factorise the result.

  • A ( 𝑎 + 𝑏 ) ( 𝑎 3 𝑏 )
  • B ( 𝑎 𝑏 ) ( 𝑎 + 3 𝑏 ) ( 𝑎 3 𝑏 )
  • C ( 𝑎 + 𝑏 ) ( 𝑎 + 3 𝑏 ) ( 𝑎 3 𝑏 )
  • D ( 𝑎 + 𝑏 ) ( 𝑎 + 3 𝑏 )
  • E ( 𝑎 3 𝑏 )

Q9:

Factorise fully 1𝑥+14𝑥𝑦49𝑦.

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

Q10:

Factorise fully 𝑎+𝑏+𝑎+𝑏.

  • A ( 𝑎 + 𝑏 ) 𝑎 + 𝑎 𝑏 + 𝑏 1
  • B ( 𝑎 + 𝑏 ) 𝑎 𝑎 𝑏 + 𝑏 + 1
  • C ( 𝑎 𝑏 ) 𝑎 + 𝑎 𝑏 + 𝑏 + 1
  • D ( 𝑎 + 𝑏 ) 𝑎 𝑎 𝑏 + 𝑏

Q11:

Factorise fully 𝑥+4𝑥𝑥4.

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

Q12:

Factorise fully 4𝑥(𝑥+2)16𝑥32𝑥.

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

Q13:

Factorise fully 𝑥(𝑦5)9𝑥(𝑦5)+18𝑦90.

  • A ( 𝑦 5 ) ( 𝑥 + 2 ) ( 𝑥 + 9 )
  • B ( 𝑦 + 5 ) ( 𝑥 6 ) ( 𝑥 3 )
  • C ( 𝑦 5 ) ( 𝑥 6 ) ( 𝑥 3 )
  • D ( 𝑦 5 ) ( 𝑥 + 1 ) ( 𝑥 + 1 8 )
  • E ( 𝑦 5 ) ( 𝑥 + 6 ) ( 𝑥 + 3 )

Q14:

Factor the expression 3𝑝𝑛+1𝑛1 completely.

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

Q15:

Factor the expression 𝑥(2𝑥+5)+2𝑥+5 completely.

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

Q16:

Factorise fully 𝑥+10𝑥+40𝑥+4𝑥.

  • A 𝑥 ( 𝑥 + 1 0 ) 𝑥 + 4
  • B 𝑥 ( 𝑥 1 0 ) 𝑥 + 4
  • C 𝑥 ( 𝑥 + 4 ) 𝑥 + 1 0
  • D 𝑥 ( 𝑥 4 ) 𝑥 + 1 0
  • E 𝑥 + 1 0 𝑥 + 4

Q17:

Factorise fully 4𝑥+8𝑥325𝑥𝑦+10𝑦.

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

Q18:

If 𝑎+20𝑏=11 and 𝑥+𝑦=3, what is the value of 𝑎𝑥+𝑎𝑦+20𝑏𝑥+20𝑏𝑦?

  • A 34
  • B 33
  • C 14
  • D 53

Q19:

Factorise fully 𝑧𝑏𝑧𝑥+𝑏𝑥.

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

Q20:

Factorise fully 4𝑥𝑎+𝑥𝑏+4𝑦𝑎+𝑦𝑏.

  • 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 )

Q21:

Factorise fully 5𝑧15𝑦𝑏𝑧+3𝑏𝑦.

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

Q22:

Factorise fully 𝑦𝑥+4𝑥+6𝑦+24.

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

Q23:

Factorise fully 9𝑥𝑚4𝑙𝑧+4𝑙𝑥9𝑚𝑧.

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

Q24:

Factorise fully 𝑥𝑦𝑛+𝑦𝑛𝑥𝑛1.

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

Q25:

Factorise fully 𝑥𝑧+15𝑦𝑢3𝑧𝑦5𝑥𝑢.

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

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