Algebraic expressions are collections of numbers, variables and operations. When an equals sign is added, they become equations.

The variables are important, as it is not an algebraic equation without them – they make the outcome different depending on their value.

Letters and numbers are called terms in algebra. For example, in 6*x*-4, the terms are -4 and 6*x*.

Of course, having too many terms can be long and unwieldy, so we simplify expressions by collecting ‘like terms’ together. Like terms are terms with the same letter. 5*x* and -3*x* are like terms. Simplified together, they make 2*x*. We can all agree that 11*x *– 2y is better than 14*x – x + *5y – 2*x* – 7y.

But not all expressions are nice and respectful and have only addition and subtraction; some have *multiplication *and *division*! Multiplication can be simplified by changing it into indices. t* *x t* *x t* *= t^{3}

When you have both multiplication and number/letter terms, you multiply the numbers and letters separately, then put them back together.

3*x* x 5*x* = 15*x ^{2}*

Simplifying division is a bit harder.

Firstly, you turn the expression into a fraction.

6t^{2}*s ^{4 }*÷ 3ts

^{2}makes

Then, you divide. You divide the numbers by each other first, and then you divide the letters by cancelling out the variables which appear on both sides.

This makes 2ts

*.*

^{2}### EVALUATING

Evaluating expressions is simple. It is merely replacing letters with numerical values and turning the expression into an equation.

If I had the equation 2s + 3*x*^{2} and s = 4 and x = 6, it would make the expression,

2 x 4 + 3 x (6×6)

Then, I turn it into an equation, by adding an equals sign and balanced answer, in this case 80.