Multiplying Brackets
Method 1 - The arrows method
2×4+2×5+3×4+3×5
=8+10+12+15
=45
Method 2 – The woman with the big nose
The woman with the big nose.
2×4+2×5+3×4+3×5
=8+10+12+15
=45
Method 3 – The box method
(2+3)(4+5)
Stage 1
|
4 |
5 |
2 |
|
|
3 |
|
|
Now multiply the rows with the columns.
Stage 2
|
4 |
5 |
2 |
8 |
10 |
3 |
12 |
15 |
Now take the numbers out of the boxes.
=8+10+12+15
=45
Method 4 - A visual way to remember multiplying out brackets
(a+b)2=a2+2ab+b2
Which can be visualised as follows:
Then
But we want a+b squared
So lets make a square
Now fill in the box
The area of each square is:
So the area of this square is a2+ab+ab+b2
Which equals
a2+2ab+b2
So that's why
(a+b)2=a2+2ab+b2
Examples
All four methods work but we will use method 1
1. Multiply out (a+b)(c+d)
ac+ad+bc+bd
Answer: (a+b)(c+d)=ac+ad+bc+bd
2. Multiply out (5x+4y)(3x-4y)
5x×3x+5x(-4y)+4y×3x+4y(-4y)
15x-20xy+12xy-16y2
15x-8xy-16y2
Answer: (5x+4y)(3x-4y)=15x-8xy-16y2
3. Multiply out (x+8)2
This is the same as (x+8)(x+8)
x2+8x+8x+8×8
x2+16x+64
Answer: (x+8)2=x2+16x+64
4. Multiply out 3(4x-7)
3×4x-3×7
12x-21
Answer: 3(4x-7)=12x-21
5. Multiply out 3xy(2x+y2)
3xy×2x+3xy×y2
3×x×y×2×x+3×x×y×y×y
6x2y+3xy3
Answer: 3xy(2x+y2)=6x2y+3xy3