Mammoth Memory

Multiplying Brackets

Method 1 -  The arrows method

1-01.jpg

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

`=8+10+12+15`

`=45`

 

Method 2 – The woman with the big nose

2-01.jpg

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

But why?

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 `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)`

3-01.jpg

`ac+ad+bc+bd`

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

 

2.  Multiply out `(5x+4y)(3x-4y)`

4-01.jpg

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

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

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

 

3.  Multiply out `(x+8)^2`

This is the same as `(x+8)(x+8)`

5-01.jpg 

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

`x^2+16x+64`  

 

4.  Multiply out `3(4x-7)`

6-01.jpg

`3times4x-3times7`

`12x-21`

 

5.  Multiply out `3xy(2x+y^2)`

7_2.jpg

`3xytimes2x+3xytimesy^2`

`3timesxtimesytimes2timesx+3timesxtimesytimesytimesy`

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

 

 

 

More Info