Properties of addition and multiplication

Learning Objectives Identify the commutative, associative, and distributive properties in algebraic expressions. Apply the properties of addition and multiplication to simplify polynomial and radical expressions. Justify each step in simplifying an algebraic expression by naming the property used. Differentiate between the commutative and associative properties. Use the identity and inverse properties to solve equations and simplify expressions. Correctly apply the distributive property to expressions involving negative signs and multiple variables. Ever noticed that when you're shopping, it doesn't matter if you buy the apples then the bananas, or the bananas then the apples? The total cost is the same! 🛒 These 'rules' also apply to algebra. This tutor...

TermDefinitionExample Commutative PropertyThis property states that the order in which you add or multiply two numbers (or terms) does not change the result.For addition: 5x + 3 = 3 + 5x. For multiplication: (2y) * 4 = 4 * (2y). Associative PropertyThis property states that the way you group three or more numbers (or terms) when adding or multiplying does not change the result. The order stays the same, but the parentheses move.For addition: (x^2 + 2x) + 5 = x^2 + (2x + 5). For multiplication: (3 * 4y) * z = 3 * (4y * z). Distributive PropertyThis property allows you to multiply a sum by multiplying each addend separately and then adding the products. It's the key to expanding expressions with parentheses.5(x - 3) becomes 5 * x - 5 * 3, which simplifies to 5x - 15. Identity PropertyT...

Commutative Properties For any real numbers a and b: a + b = b + a and a * b = b * a Use this to reorder terms in an expression, often to group like terms together before combining them. Associative Properties For any real numbers a, b, and c: (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c) Use this to regroup terms. This is especially useful in multiplication to make calculations easier, like in (2x * 50) * 7. Distributive Property For any real numbers a, b, and c: a(b + c) = ab + ac Use this to eliminate parentheses by 'distributing' the factor outside to every term inside. This is fundamental for multiplying polynomials.