Identify equivalent expressions

Learning Objectives Define 'expression', 'variable', 'constant', and 'equivalent expressions'. Apply the commutative and associative properties to rearrange terms in an expression. Use the distributive property to rewrite expressions. Combine like terms to simplify expressions. Determine if two expressions are equivalent by simplifying them. Verify the equivalence of expressions by evaluating them for specific variable values. Have you ever seen two different ways to say the same thing? 🤔 In math, expressions can look different but still mean the exact same thing! Let's find out how! In this lesson, you'll learn what makes two algebraic expressions 'equivalent' and discover powerful properties that help us transfo...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols, but no equals sign.$3x + 5$ VariableA letter or symbol used to represent an unknown number or a quantity that can change.In $2y - 7$, 'y' is the variable. ConstantA number in an expression whose value does not change.In $4x + 9$, '9' is the constant. TermThe parts of an expression that are separated by addition or subtraction signs.In $5x + 2y - 10$, the terms are $5x$, $2y$, and $-10$. CoefficientThe numerical factor of a term that contains a variable.In $7x$, '7' is the coefficient. In $y$, the coefficient is '1'. Like TermsTerms that have the same variable raised to the same power. Constants are also like terms.$3x$ and $7x$ are like...

Commutative Property of Addition $a + b = b + a$ You can change the order of numbers when adding without changing the sum. This helps rearrange terms. Commutative Property of Multiplication $a imes b = b imes a$ You can change the order of numbers when multiplying without changing the product. This helps rearrange factors within a term. Associative Property of Addition $(a + b) + c = a + (b + c)$ You can change the grouping of numbers when adding without changing the sum. This helps combine terms in different orders. Distributive Property $a(b + c) = ab + ac$ To multiply a number by a sum, you can multiply the number by each part of the sum separately and then add the products. This is key for expanding expressions.