Simplifying an expression

Simplifying means writing an expression using as few terms as possible, without changing its value.

Grouping like terms

You can only group terms that are of the same type:

3x + 2x  =  5x          (3 times x plus 2 times x is 5 times x)
4a + 3 - a  =  3a + 3   (‘a's with ‘a's', numbers with numbers)

On the other hand:

3x + 2   reste  3x + 2

There’s nothing we can do here: 3x and 2 are not of the same kind. It’s like trying to add 3 apples and 2 pears — the result is written as ‘3 apples and 2 pears’.

The analogy that works

Treat the letter as a unit. 3x + 2x is ‘3 metres + 2 metres = 5 metres’. Nobody would question that addition.

Watch out for powers

3x + 2x     =  5x
3x x 2x     =  6x^2
x^2 + x     reste  x^2 + x

x and x^2 are not of the same nature either: they are not grouped together.

The minus sign before a set of brackets

This is the most common pitfall in the whole chapter:

5 - (x + 2)  =  5 - x - 2  =  3 - x

The minus sign applies to everything inside the brackets, not just the first term. Writing 5 - x + 2 is incorrect.