Vocabulary

## Vocabulary

There are a number of words that algebra uses:

term is a variable, or a combination of variables. It may be multiplied by a number (called a coefficient) and parts of it be to a power: x, 3x, 5x^2, 7ab and frac(1)(2)a^2b are all terms;

an expression is a collection of more than one term: 3x + 5y is an expression, as is 2x^2 - 5x. There is normally an addition or a subtraction involved, and the combinations of variables are not the same. An expression does not have an equals sign;

an equation has an equals sign, and the value of the variable, or letter, can be worked out by solving the equation. 5x - 3 = 2 is an equation: the value of x can be solved;

formula determines one value given other values. Although it has an equals sign, it differs from an equation because the other values determine the value of the unknown. A = frac(1)(2)bh is a formula.

an inequality gives a set of answers for an algebraic statement. For example, x > 12 is an inequality: and 13, 14, 15, 16 are all valid answers for that statement.

Higher students: an identity is an expression that is written in another form.

x^2 + x - 6 = (x + 3)(x - 2) is an identity:

whichever value of x is chosen, the equation remains true. It is not possible to find a solution to an equation if it is an identity.

## Example 1

Is 3x^2 + 4xy a term, an expression or a formula?

There is more than one term, as shown by the plus sign. There is no equals sign which stops it being a formula or an equation.

Is d = vt + frac(1)(2)at^2 an equation or a formula?
You can work out the value of d given the other values.