Factorising into a single bracket

The Maths Habit

1Expand 2(x + 6)
2x + 12
2Expand 5(x − 2)
5x − 10
312 ÷ 3
4

Sam packs all of this into party bags. Every bag is the same. Every bag gets one cake. How many bags? What goes in each bag?

Sam hasParty bags?

3 bags. A cake and 2 sweets in each bag.

x+
Term
One part of an expression. Terms are joined by + or − signs.
xxx3
Common factor
A number that goes into every term.
3x
Factorise
Write an expression with a bracket. It is the opposite of expand.

Factorise 3x + 6

xxx3x+6
3 x bars and 6 squares
×3x+6
1Find the common factor
3
3
One x bar in each row: 3 rows.
2Divide each part
x+2
x+2
Each row is x + 2.
Answer3(x + 2)

Write the expression for these tiles.

xx 2x + 10

Which is right?

3x + 21
3(x + 21)3(x + 7)
3(x + 7): divide each part

Factorise 4x + 20

xxxx
2Divide each part
×x+5
1Find the common factor
44x+20
Answer4(x + 5)

Factorise 2x + 6

xx
2Divide each part
×x+3
1Find the common factor
22x+6
Answer2(x + 3)

Factorise 4x + 20

xxxx
2Divide each part
×x+5
1Find the common factor
44x+20
Answer4(x + 5)

Factorise 5x + 30

xxxxx
2Divide each part
×x+6
1Find the common factor
55x+30
Answer5(x + 6)
Remember1Find the common factor2Divide each part×221

Factorise 4x + 20

xxxx
2Divide each part
×x+5
1Find the common factor
44x+20
Answer4(x + 5)

Factorise 2x + 14

xx
2Divide each part
×x+7
1Find the common factor
22x+14
Answer2(x + 7)
Remember1Find the common factor2Divide each part×221

Factorise 4x + 20

xxxx
2Divide each part
×x+5
1Find the common factor
44x+20
Answer4(x + 5)

Factorise 4x + 16

xxxx
2Divide each part
×x+4
1Find the common factor
44x+16
Answer4(x + 4)
Remember1Find the common factor2Divide each part×221

Factorise 2x + 18

xx
2
×x+9
1
22x+18
Answer2(x + 9)

Factorise 3x + 18

xxx
2
×x+6
1
33x+18
Answer3(x + 6)

Factorise 5x + 25

xxxxx
2
×x+5
1
55x+25
Answer5(x + 5)
Remember1Find the common factor2Divide each part×221

xxxx
  • A dashed square takes away 1.
  • 4x − 12 is 4 rows of x − 3.
  • Keep the − with the 3 on top of the grid: −3.

What goes on top of the grid?

3x − 9xxx x and −3

Factorise 4x − 12

xxxx
2Divide each part
×x−3
1Find the common factor
44x−12
Answer4(x − 3)

Factorise 2x − 8

xx
2Divide each part
×x−4
1Find the common factor
22x−8
Answer2(x − 4)

Factorise 4x − 12

xxxx
2Divide each part
×x−3
1Find the common factor
44x−12
Answer4(x − 3)

Factorise 5x − 15

xxxxx
2Divide each part
×x−3
1Find the common factor
55x−15
Answer5(x − 3)
Remember1Find the common factor2Divide each part×221

Factorise 4x − 12

xxxx
2Divide each part
×x−3
1Find the common factor
44x−12
Answer4(x − 3)

Factorise 3x − 15

xxx
2Divide each part
×x−5
1Find the common factor
33x−15
Answer3(x − 5)
Remember1Find the common factor2Divide each part×221

Factorise 4x − 12

xxxx
2Divide each part
×x−3
1Find the common factor
44x−12
Answer4(x − 3)

Factorise 4x − 20

xxxx
2Divide each part
×x−5
1Find the common factor
44x−20
Answer4(x − 5)
Remember1Find the common factor2Divide each part×221

Factorise 2x − 14

xx
2
×x−7
1
22x−14
Answer2(x − 7)

Factorise 5x − 20

xxxxx
2
×x−4
1
55x−20
Answer5(x − 4)

Factorise 3x − 18

xxx
2
×x−6
1
33x−18
Answer3(x − 6)
Remember1Find the common factor2Divide each part×221

Factorising into a single bracket worksheet, page 1

Factorising into a single bracket worksheet, page 2

Answer sheet

Is it factorised right? Thumbs up: yes. Thumbs down: no.

  1. 2x + 16 = 2(x + 8)

    Yes

  2. 5x + 35 = 5(x + 35)

    No: 5(x + 7)

  3. 4x − 24 = 4(x + 6)

    No: 4(x − 6)

  4. 10x + 20 = 10(x + 2)

    Yes

  5. 3x − 27 = 3(x − 9)

    Yes

  1. Find the missing number. 6x + 30 = 6(x + □)

    5

  2. Factorise 6x + 9. Hint: 3 goes into both.

    3(2x + 3)

  3. Dan factorises 12x + 8 as 2(6x + 4). Dan has not finished. Finish it.

    4(3x + 2)

  1. Factorise 2x + 12. Step 1 is given: the common factor is 2.

    Answer 2(x + 6)
    xx

  2. Factorise 5x − 25

    Answer 5(x − 5)
    xxxxx

  3. Factorise 10x + 40

    Answer 10(x + 4)
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