Factoring

When a question is written as "Factor the following expression" or simply "Factor ..." all you have to do is re-write the expression given as 2 numbers or expressions multiplied by each other.

Factor 12:
12 = 2 × 6 or 2(6)
or
12 = 3 × 4 or (3)(4)
... where the brackets imply multiplication.

You can always check your answer by multiplying it out - but make sure you know the difference between your answer and your check.

Factor 2x + xy
Do this by finding the HCF of both parts of the expression (in this case x) and then rewriting the expression as
x(2+y) (<= This is the answer)
x(2+y) = 2x + xy (<= This is the check)

Look back in the orange and purple books for a revision of factoring.

For question 7:
Remember that you have to put (3x ....) into the first bracket and (x ....) into the second one. When you multiply these out that'll give you 3x².
Then remember that when you are looking for 2 numbers that multiply to give -8, you will be multiplying one by 3 and one by 1 to get them to add to +2.
For questions 8 and 9:
Both must be difference of 2 squares. Remember that 1 = 1².

For question 10:
In this one, you might not realise that you are finished when you take out the HCF - but that is all there is to it.

I'll start question 31 from the set work here.
2x(2x-y)+y(2x-9y)
= 4x² - 2xy + 2xy - 9y²
-2xy + 2xy cancel each other out so you are left with a familiar looking
4x² - 9y² to factor.

Note also the questions from 22 to 30:
The tip is at the top of the page - we don't have a single rule for factoring something like this is one go, so see if you can simplify it by factoring out something as a first step. This means we'll end up with 3 factors. Like saying that 24 = 2 × 3 × 4.
So for 5x² - 20y² we first take the HCF which is 5 and write down
5x² - 20y²
= 5(x² - 4y²)
= 5((x)² - (2y)²)
= 5(x-2y)(x+2y)