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Evaluate expressions by substitution

Evaluating an expression by substitution means replacing each variable with its given numerical value while preserving the expression’s structure, then calculating with parentheses, exponents, and the agreed order of operations. The understanding applies to expressions involving whole numbers, integers, fractions, and decimals, and distinguishes finding an expression’s value from solving an equation; it does not include symbolic simplification, advanced exponent rules, or complex rational expressions.

Detailed Explanation: Evaluate expressions by substitution

To evaluate an expression by substitution:

  1. Replace each variable with its given value.
  2. Put negative numbers in parentheses.
  3. Calculate using the order of operations: parentheses, exponents, multiplication or division, then addition or subtraction.

Example: Evaluate 3x2−2y3x^2-2y when x=−2x=-2 and y=3y=3.

Substitute the given values for the variables:

3(−2)2−2(3)3(-2)^2-2(3)

Now evaluate the exponent:

3(4)−2(3)3(4)-2(3)

Multiply:

12−612-6

Subtract:

6\boxed{6}

So, the value of 3x2−2y3x^2-2y is 6\boxed{6}. Evaluating finds the value of an expression; it does not mean solving an equation.

Learn by doing: Evaluate expressions by substitution

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    Algebraic Function Variable Substitution - Fractional Terms (Negatives)

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