Multiply polynomials

Learning Objectives Multiply a monomial by a polynomial using the distributive property. Multiply two binomials using the distributive property (including the FOIL method). Multiply two binomials using the area model (box method) for organization. Multiply polynomials with more than two terms, such as a binomial by a trinomial. Simplify the resulting expression by correctly combining like terms. Apply polynomial multiplication to solve real-world problems, such as finding the area of a shape with variable dimensions. Recognize and apply special product patterns, including the difference of squares and perfect square trinomials. Ever wondered how to calculate the area of a garden if you only know its length and width are 'a little bigger than x'? 🤔 Let's fin...

TermDefinitionExample PolynomialAn expression made up of variables, constants, and exponents, combined using addition, subtraction, and multiplication. The exponents must be non-negative integers.3x^2 + 2x - 5 is a polynomial. MonomialA polynomial with only one term.7x or -4y^3 BinomialA polynomial with two terms.x + 5 or 2a^2 - 9 TrinomialA polynomial with three terms.x^2 + 6x + 8 Like TermsTerms that have the exact same variables raised to the exact same powers. Only the coefficients (the numbers in front) can be different.5x^2 and -2x^2 are like terms, but 5x^2 and 5x are not. Distributive PropertyThe rule that states multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.4(x + 2) = 4*x + 4*2 = 4x + 8

Product Rule for Exponents x^a * x^b = x^(a+b) When multiplying two terms with the same base, you keep the base and add the exponents. The Distributive Property a(b + c) = ab + ac This is the fundamental rule for multiplying polynomials. Every term in the first polynomial must be multiplied by every term in the second polynomial. FOIL Method (for Binomials) (a + b)(c + d) = ac + ad + bc + bd A mnemonic for distributing two binomials. Multiply the First terms, Outer terms, Inner terms, and Last terms, then combine like terms.