Overview
Evaluation replaces every occurrence of a variable with its assigned value. Parentheses preserve a substituted negative value, especially inside a power. An expression may contain several dependent operations, so write the substituted expression before arithmetic.
Consider this example: Evaluate 2x² − 3y when x = −2 and y = 5. Substitute to obtain 2(−2)² − 3(5) = 8 − 15 = −7. Treating (−2)² as −4 instead gives −23.
The method also handles a different case: Evaluate (a − b)/(a + b) when a = 3/2 and b = −1/2. The numerator is 3/2 − (−1/2) = 2, and the denominator is 1. Thus the quotient is 2. Using the same subtraction in both numerator and denominator would incorrectly give 1.
For a further application, consider: A rectangle has width w and length 2w + 1. What is its area when w = 3/2? The length is 2(3/2) + 1 = 4. Multiply length by width to get 4(3/2) = 6 square units. Adding the dimensions would calculate neither area nor perimeter.
Squaring a negative input without parentheses can turn a positive square into a negative value. Replacing only the first occurrence of a variable leaves the evaluation incomplete. On a new expression, count the occurrences of each variable and substitute all of them. Estimate the sign of each term and check denominator restrictions before dividing.