Addition and Subtraction
To simplify algebraic expressions using addition and subtraction, recognise the like terms, then add or subtract accordingly.
To multiply algebraic expressions, multiply numbers with numbers and letters with corresponding letters. Powers of the terms you multiply are added, hence:
In division, the powers of corresponding like terms are subtracted. Notice that this is the opposite of multiplication.
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
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.
Order refers to indices, powers or exponents - these take the second priority.
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.
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.