## Simplifying Expressions

### Multiplying Terms

3x means "3 multiplied by x". The multiplying sign is not shown.

If two terms are being multiplied, the number comes first and the variables are usually placed in alphabetical order.

Examples

3q × 4p = 12pq
5a × 6b × 2 = 60ab

Note that in these two examples, the numbers are first and letters (variables) are placed in alphabetical order.

If the variables are the same then exponents are used. (See Topic 37)

Remember 3x.4y means 3x multiplied by 4y (which equals 12xy).

An expression involving addition and subtraction can be simplified only if it contains liketerms.

Like terms have the same variables (letters) and exponents (indices)

Examples

{ 2a, 4a, -6a } are like terms. a is common to all.
{ x, 3a2, 6 } are unlike terms. There is no common term.

The like terms are collected together and then added or subtracted.

 Examples Like or unlike terms? Answers Simplify: 4a + 6a like terms 4a + 6a = 10a 12x − 3x like terms 12x − 3x = 9x 12pq + 4pq like terms 12pq + 4pq = 16pq 12x2 + 10x2 like terms 12x2 + 10x2 = 22x2 3p + 4q unlike terms 3p + 4q cannot be simplified. 4b + 5b2 unlike terms 4b + 5b2 cannot be simplified. 3c + 4d + 5c some like terms 3c + 4d + 5c = 3c + 5c + 4d= 8c + 4d(cannot be simplified further)

### The Order of Variables and Terms

In a term the variables are usually placed in alphabetical order although the terms are still equal if the variables are not in alphabetical order.

e.g. ab = ba

6pq2 = 6q2p

In an expression the terms can also be arranged in a different order so long as the operation sign moves too.

e.g. a + b = b + a

p − 2q = -2q + p

### Dividing Terms

Dividing terms is covered in the extension topic, More Difficult Algebra, Topic 50