Algebraic Rules and Terms

The study of algebra becomes a little easier once you understand the basic rules.

Here are some examples:

a³ means a x a x a (but 3a means a + a + a).

bd³ means b x d x d x d (you only cube the d).

3y² means 3 x y x y (you only square the y).

(bd)³ means b x d x b x d x b x d.

   f      means f  ÷ c

   c

Algebraic Terms

Algebraic terms are separated by + and – signs.

A coefficient is a number or letter multiplying a term. For example:

4x – 3y + 2 x²y

                  5

4x the coefficient of x is 4.

3y the coefficient of y is -3.

2 x²y  the coefficient of x²y  is 2

5                                                          5

The above term could be written as 0.4 x²y   but we usually use fractions as coefficients.

Simplifying Algebraic Expressions

An expression is a collection of algebraic terms and like terms have the same combination of letters. See the example below:

8b + 3bd + 5bd – 5b

8b and -5b are like terms so they can be collected to give 3b.

3bd and 5bd are also like terms so they can be collected to give us 8bd.

So 8b + 3bd + 5bd – 5b = 3b + 8bd.

Combinations of letters that are not the same as said be to unlike terms, so for example:

3xy and xy² are unlike terms and they can’t be added together.

Key phrases to remember:

Term – a single number of variable or numbers and variables multiplied together.

Coefficient – the number occurring at the start of each term.

Expression – a collection of terms.

Indices (powers) – a convenient way to write repetitive multiplications.

Identity – an equation that is true for all values.