# Algebra - Basic Definitions

*It may help you to read Introduction to Algebra first*

## What is an Equation

An equation says that two things are equal. It will have an equals sign "=" like this:

x |
+ |
2 |
= |
6 |

That equation says: **what is on the left (x + 2) is equal to what is on the right (6)**

So an equation is like a **statement** "*this* equals *that*"

## Parts of an Equation

So
people can talk about equations, there are **names** for different parts (better than saying "that thingy there"!)

Here we have an equation that says 4x − 7 equals 5, and all its parts:

A **Variable** is a symbol for a number we don't know yet. It is usually a letter like x or y.

A number on its own is called a **Constant**.

A **Coefficient** is a number used to multiply a variable (**4x** means **4** times **x**, so **4** is a coefficient)

Variables on their own (without a number next to them) actually have a coefficient of 1 (**x** is really **1x**)

Sometimes a coefficient is a letter like **a** or **b** instead of a number:

### Example: ax^{2} + bx + c

**x**is a variable**a**and**b**are coefficients**c**is a constant

An **Operator** is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values).

A **Term** is either a single number or a variable, or numbers and variables multiplied together.

An **Expression** is a group of terms (the terms are separated by + or − signs)

So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

## Exponents

The** **exponent (such as the 2 in x^{2}) says **how many times **to use the value in a multiplication.

### Examples:

8^{2} = 8 × 8 = 64

y^{3} = y × y × y

y^{2}z = y × y × z

Exponents make it easier to write and use many multiplications

Example: **y ^{4}z^{2}** is easier than

**y × y × y × y × z × z**

## Polynomial

Example of a Polynomial: **3x ^{2} + x - 2**

A polynomial can have **constants**, **variables** and the **exponents 0,1,2,3,...**

But it never has division by a variable.

## Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

## Like Terms

Like Terms are **terms** whose variables (and their exponents such as the 2 in x^{2}) are the same.

In other words, terms that are "like" each other. (Note: the **coefficients** can be different)

### Example:

(1/3)xy^{2} |
−2xy^{2} |
6xy^{2} |

Are all **like terms** because the variables are all **xy ^{2}**