Basic algebra

Basic algebra

Algebra uses letters or symbols to represent numbers so the same rule that apply to numbers also apply to algebra. However, there are specific rules used for addition and subtraction in algebra and specific rules for multiplication and division in algebra.

Addition and subtraction

Algebra uses letters or symbols to represent numbers so the same rule that apply to numbers also apply to algebra. However, there are specific rules used for addition and subtraction in algebra and specific rules for multiplication and division in algebra.

As can be seen all multiples of a are like terms but the square of a only occurs once so cannot be added. Similarly all multiples of b are like terms but the square b only occurs once so cannot be added to any other term. Also 3c only occurs once so cannot be added to any other term.

Answer

Note:

All terms that occur once must remain in the final answer as shown above. The answer is shown after the equals sign.

Exercise 1

Exercise 2

Multiplication and division

The rules for multiplication and division of algebraic terms are different from addition and subtraction of terms. Firstly, it is important to understand the result of multiplying positive and negative terms. These are shown below:

+ × + = +

- × - = +

- × + = -

The easiest way to remember this is that only a negative times a positive gives a negative term, the other 2 combinations give a positive term. The same rule applies to division of terms.

Secondly, when multiplying terms raised to a power the rules of indices apply as given below:

Multiplication