These words can be confused with each other.

Equation: An equation looks like this, x+3=5, the difference between this and an expression is the equal sign (=)

Formula: A formula is a special type of equation; it shows the relationship between two variables. A formula looks like this, v=hwl, when v = volume, h = height, w = width and l = length. x+3=5 is not a formula, it has only one variable x.

Identity:  An identity is a relation which is true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of the involved variables.

Expression: An expression shows a mathematical relationship whereby there is no solution.
For example, the expression 5x + 6 can be intepreted in many ways:

If x = 5, the value of the expression is 31. To work this out you replace x with 5, so you get ( 5 x 5) + 6 = 31

If x = - 3, the value of the expression is (5 x -3) + 6 = -15 + 6 = -9

Examples:

3x+4= 19  This is an equation.

1/2b(a+b)h   This is a formula.

Sin2(Ө)+ cos2(Ө)≡ 1   This is an identity.

7x-3   This is an expression.

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