Factorisation is putting things back into brackets. For example:
6x+12
First of all, we need to find the highest common factor (HCF). In this case it is 6. Next, we need to divide the numbers by the HCF. So 6÷6=1 and 12÷6=2. Now, to find our answer, we take the HCF (6) and put it in front. Next, we take our divided numbers (1 and 2) and put them inside some brackets. If there are any letters (e.g. x or y) make sure to put them in too. So our answer will be this:
6(x+2)
Substitution is when you substitute a number with a letter, a bit like a blank Scrabble tile. For example:
If x=4, what is 2x?
Remember that if you see a number and a letter together, there is a hidden times sign between them. So 2x is actually 2 × x. So, if x=4, 2x would mean 2 × 4. So our answer would be 8.
Simplifying expressions (also known as 'collecting like terms') is when you take an expression and break it down into its simplest form. For example:
x+x
This is a very simple one, so we'll do some more afterwards. Remember that x is the same as 1x, so x+x is the same as 1x+1x. We don't do anything with the Xs, we just add the 1s - 1+1=2, so our answer is 2x. Here's another:
3x+5y+2x+4y
This one looks difficult but it isn't. Remember that we can't add an x to a y, so the simplest expression will have to include Xs and Ys. So first we'll add the Xs - 3x+2x=5x. And now the Ys - 5y+4y=9y. So our simplest expression is 5x+9y because we can't add Xs and Ys together.
