Evaluate multi variable expressions

Learning Objectives Define key terms related to algebraic expressions, such as variable, term, and coefficient. Correctly substitute given numerical values for variables in an algebraic expression. Apply the order of operations (PEMDAS/BODMAS) accurately when evaluating multi-variable expressions. Evaluate multi-variable expressions involving positive and negative integers. Evaluate multi-variable expressions that include exponents and grouping symbols. Simplify multi-variable expressions to a single numerical value after substitution. Identify and correct common errors made when evaluating expressions. Ever wonder how engineers calculate the strength of a bridge, or how scientists predict the path of a rocket? 🚀 They use expressions that change based on different conditi...

TermDefinitionExample VariableA letter or symbol that represents an unknown or changing numerical value in an expression or equation.In the expression `3x + 5`, 'x' is the variable. Algebraic ExpressionA mathematical phrase that contains variables, numbers, and at least one operation (like addition, subtraction, multiplication, or division). It does not contain an equals sign.`2a + 7b - 4` is an algebraic expression. TermThe parts of an algebraic expression that are separated by addition or subtraction signs.In `5x - 2y + 8`, the terms are `5x`, `-2y`, and `8`. CoefficientThe numerical factor that multiplies a variable in a term.In `7m`, '7' is the coefficient. In `-3xy`, '-3' is the coefficient. ConstantA term in an algebraic expression that does not contain...

Substitution Principle Replace each variable in the expression with its assigned numerical value. This is the first step in evaluating any algebraic expression. Be careful to replace *every* instance of a variable with its correct value. Use parentheses when substituting negative numbers or expressions to avoid sign errors. Order of Operations (PEMDAS/BODMAS) 1. **P**arentheses (or **B**rackets) 2. **E**xponents (or **O**rders) 3. **M**ultiplication and **D**ivision (from left to right) 4. **A**ddition and **S**ubtraction (from left to right) After substituting values, follow this specific order to perform calculations to ensure you arrive at the correct final answer. Multiplication and division have equal priority, as do addition and subtraction; always work from left to ri...