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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.

Answer: An expression

Example 2

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.

Answer: It is a formula

See also Terms