# 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.