Identical Transformation

the replacement of one analytic expression by another that is equal to the first expression but is of different form. Identical transformations are used to put expressions in a form more convenient for carrying out numerical calculations, applying further transformations, taking logarithms, taking antilogarithms, differentiating, integrating, solving equations, and so on. Examples of identical transformations are multiplying out (removing parentheses), factoring, reducing algebraic fractions to a common denominator, decomposing algebraic fractions to sums of simple fractions, and reducing sums of trigonometric functions to a form suitable for taking logarithms (that is, transforming the sums into products).