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





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.





Method 3 – The box method


Stage 1











Now multiply the rows with the columns.


Stage 2











Now take the numbers out of the boxes.




Method 4 - A visual way to remember multiplying out brackets


Which can be visualised as follows:

Take A and B from the equation


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 `a^2+ab+ab+b^2`

Which equals



So that's why




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


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




Answer: `(5x+4y)(3x-4y)=15x-8xy-16y^2`


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 



Answer: `(x+8)^2=x^2+16x+64`  


4.  Multiply out `3(4x-7)`

This example looks difficult but is relatively easy



Answer: `3(4x-7)=12x-21`


5.  Multiply out `3xy(2x+y^2)`

Work this example out




Answer: `3xy(2x+y^2)=6x^2y+3xy^3`



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