Write equivalent expressions using properties

Learning Objectives Identify the Commutative, Associative, and Distributive Properties. Apply the Commutative Property to reorder terms in an expression. Apply the Associative Property to regroup terms in an expression. Apply the Distributive Property to expand or factor expressions. Combine like terms to simplify algebraic expressions. Write equivalent expressions using a combination of properties. Ever wonder if there's more than one way to say the same thing in math? 🤔 Just like 'six plus two' is the same as 'two plus six', expressions can look different but still have the same value! In this lesson, you'll learn how to rewrite algebraic expressions into different, but equivalent, forms using special rules called properties. Understanding t...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷) but does not have an equals sign.5x + 7 or 3(y - 2) TermParts of an expression separated by addition or subtraction signs.In the expression 4x + 3y - 2, the terms are 4x, 3y, and -2. CoefficientThe numerical factor of a term that contains a variable.In the term 7x, 7 is the coefficient. In the term y, 1 is the coefficient. ConstantA term in an expression that does not contain a variable; its value does not change.In the expression 2x + 5, 5 is the constant. Like TermsTerms that have the exact same variable part (including exponents). Constants are also considered like terms.3x and -7x are like terms. 5 and 12 are like terms. 2y and 8y are like terms. Equivalen...

Commutative Property of Addition and Multiplication $$a + b = b + a$$ $$a \cdot b = b \cdot a$$ This property states that the order in which you add or multiply numbers (or terms) does not change the sum or product. It helps us rearrange terms to group like terms together. Associative Property of Addition and Multiplication $$(a + b) + c = a + (b + c)$$ $$(a \cdot b) \cdot c = a \cdot (b \cdot c)$$ This property states that the way you group numbers (or terms) when adding or multiplying does not change the sum or product. It allows us to change the parentheses to group terms differently. Distributive Property $$a(b + c) = ab + ac$$ $$a(b - c) = ab - ac$$ This property allows you to multiply a single term by two or more terms inside a set of parentheses. You 'dis...