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

`2times4+2xx5+3xx4+3xx5`

`=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.

`2times4+2xx5+3xx4+3xx5`

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

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

Which equals

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

 

So that's why

`(a+b)^2=a^2+2ab+b^2`

 

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

`5xtimes3x+5x(-4y)+4ytimes3x+4y(-4y)`

`15x-20xy+12xy-16y^2`

`15x-8xy-16y^2`

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 

`x^2+8x+8x+8times8`

`x^2+16x+64`  

Answer: `(x+8)^2=x^2+16x+64`  

 

4.  Multiply out `3(4x-7)`

This example looks difficult but is relatively easy

`3times4x-3times7`

`12x-21`

Answer: `3(4x-7)=12x-21`

 

5.  Multiply out `3xy(2x+y^2)`

Work this example out

`3xytimes2x+3xytimesy^2`

`3timesxtimesytimes2timesx+3timesxtimesytimesytimesy`

`6x^2y+3xy^3`

Answer: `3xy(2x+y^2)=6x^2y+3xy^3`

 

 

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