Identify equivalent expressions

Learning Objectives Simplify algebraic expressions related to the perimeter and area of two-dimensional figures. Apply the commutative, associative, and distributive properties to rewrite expressions. Determine if two algebraic expressions representing geometric properties are equivalent. Justify the equivalence of expressions using algebraic properties and combining like terms. Create multiple equivalent expressions for a given geometric scenario involving variables. Evaluate expressions for specific variable values to verify equivalence. Ever wonder if there's more than one way to describe the perimeter of your backyard fence or the area of a new floor plan? 🤔 In this lesson, you'll learn how to identify and create different algebraic expressions that represent...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols, but no equality sign.$2x + 5$ or $3(l+w)$ Equivalent ExpressionsExpressions that have the same value for all possible values of the variables.$2(x+3)$ and $2x+6$ are equivalent. TermA single number, a single variable, or a product of numbers and variables within an expression, separated by addition or subtraction signs.In $3x + 5y - 7$, the terms are $3x$, $5y$, and $-7$. Like TermsTerms that have the same variables raised to the same powers. Only the coefficients can be different.$4x$ and $-2x$ are like terms; $3xy$ and $7xy$ are like terms. CoefficientThe numerical factor of a term that contains a variable.In $5x^2$, $5$ is the coefficient. In $y$, the coefficient is $1$. Co...

Distributive Property $a(b + c) = ab + ac$ To multiply a sum by a number, you can multiply each addend by the number and then add the products. This is essential for expanding expressions. Combining Like Terms $ax + bx = (a+b)x$ You can add or subtract terms that have the same variable part by adding or subtracting their coefficients. This simplifies expressions. Commutative Property of Addition $a + b = b + a$ The order in which numbers are added does not change the sum. Useful for rearranging terms to group like terms. Commutative Property of Multiplication $a \cdot b = b \cdot a$ The order in which numbers are multiplied does not change the product. Useful for rearranging factors in a term.