# Algebra - Basic Definitions

## 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: ax2 + 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 x2) says how many times to use the value in a multiplication. ### Examples:

82 = 8 × 8 = 64

y3 = y × y × y

y2z = y × y × z

Exponents make it easier to write and use many multiplications

Example: y4z2 is easier than y × y × y × y × z × z

## Polynomial

Example of a Polynomial: 3x2 + 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 x2) are the same.

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

### Example:

 (1/3)xy2 −2xy2 6xy2

Are all like terms because the variables are all xy2