# Algebra Expressions

An expression shows the relationship between numbers and variables and dimensions.

For example in the expression 4a^{2 }+ 6b - 8, the 4 means that there are 4 sets of a^{2} whilst the 6 signifies 6 sets of b and the -8 means that 8 is subtracted from the first two terms.

The a and b are known as **variables**, whilst the -8 is known as a **constant**.

A **variable** is an unknown. **Variables** are assigned letters "x," "y," "z," etc

As an example, in the equation x + y = 7 the values of x and y can be lots of different things. If x = 3 then y=4, if x=1 then y=6 etc.

The algebraic expression may have one or more **variables**. The variables may be raised to different powers. (i.e r x r x r = r^{3}, z x z x z x z = z^{4} )

A **term** is the number and the attached variable. In the expression 6x^{2} - 2y , the 6x^{2} and the -2y are terms. The 6x^{2} tells us that there are six lots of x^{2} ( i.e 6 times x^{2}) The 6 and 2 are known as **numerical coefficients**.

**Like terms** are numbers with the same variables with the same powers. So, in the expression 7m^{2 }+ 3n - 3m^{2} - 3m the **like terms** are 7m^{2} and -3m^{2}

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**Like terms** can be added and subtracted, for example 7m^{2 }+ 3n - 3m^{2} - 3m is the same as 4m^{2 }+ 3n - 3m .

**Coefficients** are numbers in front of variables. If there is not a number in front of a variable, the understood coefficient is "1." If there is a negative in front of a variable with no number in front of it, the coefficient is a negative one.

So, in the expression 4a^{2}, the 4 means 4 lots of a^{2}

The numbers that go in front^{}of variables are called **Coefficients**. If no number is before a variable then the coefficient is "1" (positive). If a negative is in front of a variable, without a number before it, then the coefficient is negative.