Distributive property

Learning Objectives Define the distributive property in their own words and identify its components. Apply the distributive property to expand algebraic expressions, including a monomial multiplied by a polynomial. Use the distributive property to multiply two binomials, leading to a quadratic expression. Apply the distributive property in reverse to factor out the greatest common factor (GCF) from a polynomial. Simplify complex expressions that involve multiple applications of the distributive property and combining like terms. Solve linear equations that require using the distributive property as an initial step. Imagine you're buying 4 value meals for your friends, and each meal includes a sandwich and a drink. 🥪🥤 How do you calculate the total items you've bo...

TermDefinitionExample TermA single mathematical expression. It can be a number, a variable, or a product of numbers and variables.In the expression `5x^2 - 3y + 7`, the terms are `5x^2`, `-3y`, and `7`. PolynomialAn algebraic expression consisting of one or more terms, where variables have whole-number exponents.`4x^3 - x + 11` is a polynomial. MonomialA polynomial with only one term.`7x` or `-2y^3` BinomialA polynomial with two terms.`x + 5` or `3a^2 - 4b` Like TermsTerms that have the exact same variables raised to the exact same powers. Only the coefficients (the numbers in front) can be different.`6x^2` and `-2x^2` are like terms, but `6x^2` and `6x` are not. FactoringThe process of breaking down a polynomial into a product of simpler expressions (its factors). It is the reverse of di...

Distributive Property over Addition a(b + c) = ab + ac To multiply a term 'a' by a sum '(b + c)', you multiply 'a' by each term inside the parentheses separately and then add the results. Distributive Property over Subtraction a(b - c) = ab - ac To multiply a term 'a' by a difference '(b - c)', you multiply 'a' by each term inside the parentheses separately and then subtract the results. Distribution with Two Binomials (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd This is often called 'double distribution' or FOIL. Each term in the first binomial is distributed to every term in the second binomial.