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:

4x-7=5: 4 is coefficient, x is variable, 7 and 5 constant, - is operator

A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y, but can be a symbol or word.

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, like +, ×, etc, that shows an operation. It tells us what to do with the value(s).


4x-7=5: 4x-7 is expression, 4x, 7 and 5 are terms

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?"


The exponent (such as the 2 in x2) says how many times to use the value in a multiplication.

8 to the Power 2


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


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:

monomial, binomial, trinomial

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)



Are all like terms because the variables are all xy2