Mammoth Memory

Multiplying Brackets

Method 1 -  The arrows method

Method 1 uses the arrow method, each arrow means you have to multiply the number at the start with the number at the end

2×4+2×5+3×4+3×5

=8+10+12+15

=45

 

Method 2 – The woman with the big nose

Method 2 on this simple equation look what shapes are being made to complete it, can you see it?

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:

Take A and B from the equation

Then

Put a and b together equaling a plus b

But we want a+b squared

So lets make a square

Draw the a and b squared on a box making b double the size of a

Now fill in the box

Fill the box with lines to separate the sections

The area of each square is:

Now fill the quarters with the corresponding values

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)

In this example multiply out the brackets using the arrow method

ac+ad+bc+bd

Answer: (a+b)(c+d)=ac+ad+bc+bd

 

2.  Multiply out (5x+4y)(3x-4y)

Multiply out this equation making sure you keep the variables together in the like terms

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)

In this example you can simplify it then multiply it out, making it easier to manage 

x2+8x+8x+8×8

x2+16x+64  

Answer: (x+8)2=x2+16x+64  

 

4.  Multiply out 3(4x-7)

This example looks difficult but is relatively easy

3×4x-3×7

12x-21

Answer: 3(4x-7)=12x-21

 

5.  Multiply out 3xy(2x+y2)

Work this example out

3xy×2x+3xy×y2

3×x×y×2×x+3×x×y×y×y

6x2y+3xy3

Answer: 3xy(2x+y2)=6x2y+3xy3