An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to ‘remove’ or ‘multiply-out’ brackets …

Let us now discuss how we can factorise expressions in one variable, like x2 + 5x + 6, y2 – 7y + 12, z2 – 4z – 12, 3m2 + 9m + 6, etc. Observe that these expressions are not of the type (a + b) 2 or (a – b) 2, …

Factors are numbers that we can multiply together to get another number. A number can have several factors. For example, 12 has the factors 1,2,3,4,6,12 To make sure that you never miss any you can …

factorise algebraic expressions, look for the highest common factor (of all terms). This common factor is brought out the front of the brackets, and remaining factors (after dividing the common factor out) …

How do I factorise expressions with common brackets? To factorise 3x(t + 4) + 2(t + 4), both terms have a common bracket, (t + 4) the whole bracket, (t + 4), can be "taken out" like a common factor

When we factorise, we tend to choose the highest common factor (the highest times table both numbers are in) so we would choose 4(2 + 3) as our answer.

Factorise x2 − 7x + 12. Hence factorise (y − 2)2 − 7(y − 2) + 12. ............................. Factorise x2 − 6x − 27. Hence factorise (y − 4)2 − 6(y − 4) − 27. ............................. Do not attempt to expand brackets. …