Identical transformations

An identical transformation is a way of changing an algebraic expression so that it looks different, but its value stays the same for all values of the variable (where the expression is defined). For example, simplifying, factoring, expanding, or combining like terms are all identical transformations.

Important properties

• Identical transformations do not change the value of the expression for any allowed value of the variable.

• They are used to simplify expressions, solve equations, or compare different forms of the same expression.

• Examples include expanding $(a+b)^2$ to $a^2 + 2ab + b^2$, or simplifying $\frac{2x}{4}$ to $\frac{x}{2}$.