Factorising Expressions - Single Brackets

It is know as factorising in England and factoring in America. They mean to put an expression into brackets. We say it has been factorised. Numbers have factors, the factors of 6 are 1, 2, 3 and 6. Expressions can also have factors like this: 6x - 12 = 3(2x - 4). Factorising is the process of finding the factors. It’s a form of simplifying, and basically just means to put into brackets. Then if we multiplied our factors together 3(2x - 4) , we’d get back to 6x - 12. Factorising is just the opposite of expanding brackets: expanding gets rid of brackets, factorising puts into brackets. To factorise, we look for the highest common factor of every part of the expression. Which was 3 in this example. Let’s look at another example: factorise 12x - 8. What is the highest common factor of 12x and -8? 2 goes into both, but it’s not the HIGHEST. We want the highest common factor, which is 4. So take 4 outside of the bracket - as that’s the highest factor: 4( ). Then what do we need to multiply 4 by to get 12x? 3x, so 3x inside the bracket: 4(3x ). And what do we need to multiply 4 by to get -8? -2, so that also goes inside the bracket: 4(3x - 2). This is the factorised expression. It is really important to check our answer - so we expand to double check ourselves. Another example: 6y^2 + 12y = 6y(y + 2). Always expand the brackets to check your answer. In this video we have just looked at factorising into one bracket, but you can factorise into 2, 3 and many more brackets.