Properties of multiplication

Learning Objectives Identify and apply the Commutative, Associative, and Distributive properties to simplify polynomial and radical expressions. Use the Distributive Property to accurately expand and factor quadratic and other polynomial expressions. Apply the Identity and Inverse Properties of Multiplication in the context of solving linear and quadratic equations. Recognize and use the Zero Product Property to find the roots of factored polynomial equations. Justify the steps of an algebraic manipulation by citing the relevant property of multiplication. Connect the properties of multiplication to the simplification of complex algebraic terms involving coefficients and variables. Ever noticed that `5 * (x + 2)` is the same as `5x + 10`? 🤔 These fundamental rules, or prope...

TermDefinitionExample Commutative Property of MultiplicationThis property states that the order in which two numbers or expressions are multiplied does not change the result.For numbers: `7 * 9 = 9 * 7`. For algebra: `(x + 4)(x - 2) = (x - 2)(x + 4)`. Associative Property of MultiplicationThis property states that when multiplying three or more numbers or expressions, the way they are grouped does not change the result.For numbers: `(2 * 5) * 6 = 2 * (5 * 6)`. For algebra: `(3x)(2y) = 3(x(2y))`. Distributive PropertyThis property links multiplication and addition/subtraction. It states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.For numbers: `5 * (10 + 2) = 5 * 10 + 5 * 2`. For algebra: `3x(x^2 - 4) = 3x^3 - 12x`. Id...

The Distributive Property For any expressions a, b, and c: `a(b + c) = ab + ac` This is the fundamental rule for expanding expressions. It is used to multiply a single term into a set of parentheses or to multiply two polynomials together (e.g., FOIL is a specific application of this property). The Zero Product Property If `a * b = 0`, then `a = 0` or `b = 0` (or both). This is a powerful property used to solve equations. If you can rewrite an equation so one side is zero and the other side is a product of factors, you can solve for each factor independently.