Evaluating Expressions by Substitution

A variable is just a placeholder. Once a problem tells you x = -2, every x in the expression becomes -2, no exceptions. The expression stops being a general rule and becomes a specific arithmetic problem with one correct numerical answer. That's the whole idea: substitution turns algebra into arithmetic.

Once the numbers are in, order of operations takes over: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right. The danger spots are exponents on negative numbers and terms with coefficients in front of a variable. Always wrap a substituted negative number in parentheses before applying an exponent, so (-2)² = 4, not -4. Multiplication signs between numbers and variables (like -4xy) mean every piece gets multiplied together once the values are in.

This skill sits underneath almost everything else on the algebra portion of the test. Remainder theorem problems ask you to evaluate a polynomial at a specific x-value to find a remainder. Function notation questions like f(3) are substitution in disguise. Checking whether a point lies on a line, a parabola, or satisfies a system also comes down to plugging numbers in and simplifying. Get substitution automatic and clean, and those other question types become mostly bookkeeping.