Factorising and Expanding Brackets

Factorising equations:

Lets look at the example:   Factorise 3x+21 

In order to factorise this equation, we need to find a common factor of both 3x and 21.  For this equation, the common factor is 3 and so this is the number that goes outside the brackets.  

We then need to work out how many times 3 goes into 3x and 21.  We know that 3x ÷ 3 = x, and 21 ÷ 3 = 7.  Therefore, 3x+21 can be factorised to give 3(x+7)

Expanding brackets: 

Lets look at the same example but in reverse order: Expand 3(x+7)

This is the opposite of factorising and so now we need to multiply each term inside the brackets by the number outside the brackets.  

First we need to multiply 3 by x which gives us 3x. 

Then we multiply 3 by 7 which gives us 21.  

Our final expansion is: 3x+21