Simplify variable expressions using properties

Learning Objectives Identify and define the Commutative, Associative, and Distributive properties. Apply the Distributive Property to expand expressions containing variables. Identify and group like terms within a variable expression. Combine like terms to simplify an expression to its most basic form. Simplify multi-step variable expressions by correctly applying the order of operations and properties of real numbers. Justify each step in the simplification process by naming the property used. Ever tried to solve a math problem that looked like a jumbled mess of letters and numbers? 🤯 Let's learn the secret rules to clean it up and make it simple! This tutorial will teach you how to use fundamental mathematical properties to simplify complex variable expressions. Mas...

TermDefinitionExample Variable ExpressionA mathematical phrase that contains at least one variable, along with numbers and operation symbols.3x² - 5y + 2 TermA single number, a single variable, or numbers and variables multiplied together. Terms are separated by + or - signs.In the expression 4a - 2b + 7, the terms are 4a, -2b, and 7. CoefficientThe numerical factor of a term that contains a variable.In the term -6k, the coefficient is -6. Like TermsTerms that have the exact same variable(s) raised to the exact same power(s). Constants are also like terms.5x and -2x are like terms. 3x² and 3x are NOT like terms. ConstantA term that does not contain any variables; its value does not change.In the expression 7x - 1, the constant is -1. SimplifyTo rewrite an expression in its most compact fo...

Distributive Property a(b + c) = ab + ac Use this to multiply a single term by a group of terms inside parentheses. This is the key to 'breaking open' the parentheses to simplify further. Commutative Property a + b = b + a and ab = ba This property allows you to change the order of terms when adding or multiplying. It's useful for grouping like terms together. Associative Property (a + b) + c = a + (b + c) and (ab)c = a(bc) This property allows you to change the grouping of terms (using parentheses) when adding or multiplying. It works with the Commutative Property to help you rearrange expressions.