Expanding single brackets

The Maths Habit

1Simplify x + x + x
3x
2How many squares?
12
3Write 5 × x with no × sign
5x

Every party bag gets what is in the first bag. Sam buys this to fill the bags. Has Sam got enough?

Every bag getsSam buysSam's bags

No. Every bag needs its sweets too.

x+
Term
One part of an expression. Terms are joined by + or − signs.
x
Bracket
Holds terms together. A number in front of it multiplies everything inside.
xxx
Expand
Multiply out the bracket, so there is no bracket left.

Expand 3(x + 2)

xxx
3 rows of x + 2
×
1Split the bracket
x+23
x+23
3 on the side. x and +2 on top.
2Multiply each part
3x+6
3x+6
3 bars make 3x. 6 squares make +6.
Answer3x + 6

How many x bars? How many squares?

xx 2 x bars and 8 squares

Which is right?

5(x + 2)
5x + 25x + 10
5x + 10: multiply each part

Expand 4(x + 6)

xxxx
1Split the bracket
×x+6
2Multiply each part
44x+24
Answer4x + 24

Expand 2(x + 6)

xx
1Split the bracket
×x+6
2Multiply each part
22x+12
Answer2x + 12

Expand 4(x + 6)

xxxx
1Split the bracket
×x+6
2Multiply each part
44x+24
Answer4x + 24

Expand 5(x + 3)

xxxxx
1Split the bracket
×x+3
2Multiply each part
55x+15
Answer5x + 15
Remember1Split the bracket2Multiply each part×11122

Expand 4(x + 6)

xxxx
1Split the bracket
×x+6
2Multiply each part
44x+24
Answer4x + 24

Expand 3(x + 4)

xxx
1Split the bracket
×x+4
2Multiply each part
33x+12
Answer3x + 12
Remember1Split the bracket2Multiply each part×11122

Expand 4(x + 6)

xxxx
1Split the bracket
×x+6
2Multiply each part
44x+24
Answer4x + 24

Expand 2(x + 10)

xx
1Split the bracket
×x+10
2Multiply each part
22x+20
Answer2x + 20
Remember1Split the bracket2Multiply each part×11122

Expand 2(x + 8)

xx
1
×x+8
2
22x+16
Answer2x + 16

Expand 3(x + 5)

xxx
1
×x+5
2
33x+15
Answer3x + 15

Expand 5(x + 6)

xxxxx
1
×x+6
2
55x+30
Answer5x + 30
Remember1Split the bracket2Multiply each part×11122

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

What goes on top of the grid?

3(x − 4)xxx x and −4

Expand 4(x − 3)

xxxx
1Split the bracket
×x−3
2Multiply each part
44x−12
Answer4x − 12

Expand 2(x − 5)

xx
1Split the bracket
×x−5
2Multiply each part
22x−10
Answer2x − 10

Expand 4(x − 3)

xxxx
1Split the bracket
×x−3
2Multiply each part
44x−12
Answer4x − 12

Expand 5(x − 2)

xxxxx
1Split the bracket
×x−2
2Multiply each part
55x−10
Answer5x − 10
Remember1Split the bracket2Multiply each part×11122

Expand 4(x − 3)

xxxx
1Split the bracket
×x−3
2Multiply each part
44x−12
Answer4x − 12

Expand 3(x − 6)

xxx
1Split the bracket
×x−6
2Multiply each part
33x−18
Answer3x − 18
Remember1Split the bracket2Multiply each part×11122

Expand 4(x − 3)

xxxx
1Split the bracket
×x−3
2Multiply each part
44x−12
Answer4x − 12

Expand 4(x − 7)

xxxx
1Split the bracket
×x−7
2Multiply each part
44x−28
Answer4x − 28
Remember1Split the bracket2Multiply each part×11122

Expand 2(x − 3)

xx
1
×x−3
2
22x−6
Answer2x − 6

Expand 5(x − 6)

xxxxx
1
×x−6
2
55x−30
Answer5x − 30

Expand 3(x − 8)

xxx
1
×x−8
2
33x−24
Answer3x − 24
Remember1Split the bracket2Multiply each part×11122

Expanding single brackets worksheet, page 1

Expanding single brackets worksheet, page 2

Answer sheet

Is the answer right? Thumbs up: yes. Thumbs down: no.

  1. 4(x + 4) = 4x + 16

    Yes

  2. 5(x + 1) = 5x + 1

    No: 5x + 5

  3. 2(x − 4) = 2x + 8

    No: 2x − 8

  4. 10(x + 5) = 10x + 50

    Yes

  5. 3(x − 3) = 3x − 9

    Yes

  1. Find the missing number. 3(x + □) = 3x + 21

    7

  2. Expand 4(2x + 3)

    8x + 12

  3. Write a bracket that expands to 6x + 12. Can you find two?

    6(x + 2) or 3(2x + 4)

  1. Expand 2(x + 7). Step 1 is given: 2 on the side, x and +7 on top.

    Answer 2x + 14
    xx

  2. Expand 5(x − 3)

    Answer 5x − 15
    xxxxx

  3. Expand 10(x + 4)

    Answer 10x + 40
Exit tickets to print