Factorising is all about converting something to "two" things multiplied.
Lets look at the starting terms:
we should know what this really means, since a lot of this is shorthand used by mathematicians. What we really have is:
or, further:
So to factor, we look at every term given... here we have just 2 terms, and we look for the most that is common to both.
So, start with the numbers. What is common? Answer is 6
Now the x's. What is common? Answer is xx
Now the y's. What is common? Answer is y
and finally the z's. what is common? Answer is z
So we shall take out 6xxyz from both terms.
What is left from the first term? Answer is 1*xxxxxx -->
And from the second term? Answer is 8yyyyyy -->
So we had 6xxyz(1xxxxxx - 8yyyyyy) which is correct but not very "professional" in its look. So we write it in a more condensed manner as:
And check: Multiply each of the terms in the bracket by and you should arrive back at the question. So get used to checking.
Now the skill is to not need the xxxxxxxyz notation. You should be able to look at and factorise it into in one line.
Now, knowing further maths skills we can spot something with the bracket: can be written as
And this is of the form of which factorises. I cannot remember this standard result, but your textbooks should quote this for you. That will give you an even more factorised version of the answer.
