How do you factorise?

Factorising is just simplyfying into brackets. To do this you need to find common terms on all the parts of the question. For example: fully factorise 3a³b+12a²b²+9a⁵b³  the answer to the is 3a²b(a+4b+3a²b²)

The common multple in this question is 3, as 3,12 and 9 are all divsible by 3. Therefore 3 goes on the outside of the brackets.... 3()

Then we look at the unknowns (a and b). All parts of the question have a², so this goes on the outside of the brackets. Similarly all parts have b, so this goes outside the brackets. Remembering that when we multiply indices the numbers add together - i.e; a² x a³ = a⁵ 

For the parts inside the brackets we try to work out how to multiply the differents parts of the orginal question to gain the answer we need. Taking the first part of the question (3a³b). On the outside of the brakets we have 3a²b and so we need to work out the difference between what we have outside the brackets to the original question - this then goes inside the brackets. In this instance the difference is a and so tha is what goes inside the bracket. This process should be repeated for each part of the orginal question and thus the question will be fully factorised.