## Addition and Subtraction

To simplify algebraic expressions using addition and subtraction, recognise the like terms, then add or subtract accordingly.

### Examples:

## Multiplication

To multiply algebraic expressions, multiply numbers with numbers and letters with corresponding letters. Powers of the terms you multiply are added, hence:

### Examples:

## Division

In division, the powers of corresponding like terms are subtracted. Notice that this is the opposite of multiplication.

### Examples:

Using cancelling or index laws to simplify divisions makes it easier. Cancel one variable on the top with another similar variable on the bottom.

## Mixture of Algebraic Operations

Different operations could be done separately in its proper order. BODMAS operations is definitely useful to remember, as well as a good knowledge of Index Laws.

BODMAS is an abbreviation of

1. **B**rackets

Any operations governed inside brackets take the highest priority. Brackets could come in many forms; e.g. parentheses, braces, square brackets; and the most inner brackets in an algebraic operation (or any function) is to be completed first.

2. **O**rder

Order refers to indices, powers or exponents - these take the second priority.

3. **D**ivision/**M**ultiplication

Then comes division and multiplication. These two take the next level of priority, however none is greater than the other. In a line of division and multiplication, complete the left first, then work your way through to the right.

4. **A**ddition/**S**ubtraction

The last priority are either addition or subtraction. Similar to division/multiplication, there is none greater than the other, start solving operations from the left to the right.

## Examples

1.

2.