Evaluating Expressions – Substitution Method

Evaluating an expression means finding its numerical value by substituting given values in place of the variables.

Substitution is the single most common operation performed in spreadsheets, engineering calculations, and scientific formulas — every time a formula like the area of a circle (A = πr²) or Einstein's E = mc² is used to compute an actual number, substitution is exactly what is happening: replacing each symbol with a known value and calculating. The negative-substitution rule below (always bracket a negative value before applying a power) trips up more students than almost any other single rule in early algebra, precisely because −2² and (−2)² look deceptively similar but evaluate to −4 and +4 respectively.

How to Evaluate

Write down the expression.
Replace each variable with its given value.
Follow BODMAS/PEMDAS to calculate.

Worked Examples

Easy: Evaluate 3x + 5 when x = 4

3(4) + 5 = 12 + 5 = 17

Medium: Evaluate 2a² − 3b when a = 3, b = 2

2(3)² − 3(2) = 2(9) − 6 = 18 − 6 = 12

Advanced: Evaluate (x + y)/(x − y) when x = 7, y = 3

(7 + 3)/(7 − 3) = 10/4 = 2.5

Negative Substitution

Evaluate x² − 4x + 3 when x = −2: (−2)² − 4(−2) + 3 = 4 + 8 + 3 = 15

Key Takeaways

Replace each variable with its value before calculating.
Use brackets when substituting negative values: −2² ≠ (−2)².
Follow order of operations after substituting.

Practice: Evaluate Expressions

Evaluate with a Negative Value