Write equivalent expressions using properties

Learning Objectives Define algebraic expressions and equivalent expressions. Identify terms, coefficients, and constants within an expression. Apply the Commutative Property of Addition and Multiplication to write equivalent expressions. Apply the Associative Property of Addition and Multiplication to write equivalent expressions. Apply the Distributive Property to write equivalent expressions. Simplify expressions by combining like terms using properties. Recognize when two expressions are equivalent. Ever wonder if there's more than one way to say the same thing in math? 🤔 Just like saying 'six plus two' or 'two plus six' means the same thing, expressions can look different but have the same value! In this lesson, you'll learn how to rewri...

TermDefinitionExample ExpressionA mathematical phrase that contains numbers, variables, and operation symbols (like +, -, ×, ÷), but does not have an equality sign (=).3x + 5 Equivalent ExpressionsExpressions that have the same value for all possible values of the variables. They look different but mean the same thing.2(x + 3) and 2x + 6 are equivalent expressions. VariableA letter or symbol (like x, y, or a) used to represent an unknown number or a quantity that can change.In the expression 3x + 5, 'x' is the variable. ConstantA number in an expression that does not change its value. It's a fixed numerical value.In the expression 3x + 5, '5' is the constant. TermThe parts of an expression that are separated by addition (+) or subtraction (-) signs.In the expressi...

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 does not change the sum or product. It helps rearrange terms. 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 when adding or multiplying does not change the sum or product. It helps rearrange parentheses. Distributive Property $$a(b + c) = ab + ac$$ $$a(b - c) = ab - ac$$ This property allows you to multiply a number by a sum or difference by multiplying that number by each term inside the parentheses. It's key for expanding expressions.