Mammoth Memory

Multiplying Brackets

Method 1 -  The arrows method

The arrow method of multiplying brackets involves drawing arrows from each number in one set of brackets to each number in the next set of brackets

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

`=8+10+12+15`

`=45`

 

Method 2 – The woman with the big nose

The woman with the big nose method of multiplying brackets, draw arrows from one set of brackets to the next set of brackets to make a face with a big nose

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:

Method 4 using lines and squares to multiply out brackets part 1

Then

Method 4 using lines and squares to multiply out brackets part 2

But we want `a+b` squared

So lets make a square

Method 4 making a square to multiply out brackets part 3 make a square

Now fill in the box

Method 4 making a square to multiply out brackets part 4 fill in the box

The area of each square is:

Method 4 making a square to multiply out brackets part 5, 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)`

Example 1 of multiplying brackets (a + b) (c + d) shown with method 1 using arrows

`ac+ad+bc+bd`

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

 

2.  Multiply out `(5x+4y)(3x-4y)`

Example 2 of multiplying brackets (5x + 4y) (3x - 4y) shown with method 1 using arrows

`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)`

Example 3 of multiplying brackets (x + 8) (x + 8) shown with method 1 using arrows 

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

`x^2+16x+64`  

Answer: `(x+8)^2=x^2+16x+64`  

 

4.  Multiply out `3(4x-7)`

Example 4 of multiplying brackets 3(4x + 7) shown with method 1 using arrows

`3times4x-3times7`

`12x-21`

Answer: `3(4x-7)=12x-21`

 

5.  Multiply out `3xy(2x+y^2)`

Example 5 of multiplying brackets shown with method 1 using arrows to show what each term is multiplied by

`3xytimes2x+3xytimesy^2`

`3timesxtimesytimes2timesx+3timesxtimesytimesytimesy`

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

Answer: `3xy(2x+y^2)=6x^2y+3xy^3`

 

 

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