Multiply monomials

Learning Objectives Identify the coefficient and variable parts of a monomial. Recall and correctly apply the Product of Powers rule for exponents. Multiply the coefficients of two or more monomials. Combine the variable parts of monomials by adding their exponents. Simplify the product of two or more monomials into a single monomial. Apply monomial multiplication to solve problems involving geometric formulas, such as the area of a rectangle. Distinguish between the rules for multiplying monomials and adding like terms. Ever wondered how to find the area of a rectangular garden if its length is `4x` meters and its width is `6x` meters? 🌱 Let's learn the simple algebra to solve this! In this tutorial, you will learn the step-by-step process for multiplying monomials...

TermDefinitionExample MonomialAn algebraic expression consisting of a single term, which can be a number, a variable, or a product of a number and one or more variables with non-negative integer exponents.`7x`, `-5a²b`, `y³`, `12` are all monomials. CoefficientThe numerical factor of a monomial.In the monomial `-5a²b`, the coefficient is `-5`. VariableA symbol, usually a letter, that represents an unknown value or quantity.In the monomial `7x`, the variable is `x`. BaseIn an expression of the form `xⁿ`, the base is the number or variable that is being multiplied by itself.In `y³`, the base is `y`. ExponentA number that indicates how many times the base is used as a factor in a multiplication.In `y³`, the exponent is `3`, meaning `y * y * y`. ProductThe result obtained after multiplying tw...

Product of Powers Rule xᵃ ⋅ xᵇ = xᵃ⁺ᵇ When multiplying two powers that have the same base, you keep the base and add the exponents. Procedure for Multiplying Monomials (axᵐ)(bxⁿ) = (a ⋅ b)xᵐ⁺ⁿ This is a two-step process: 1. Multiply the coefficients. 2. Multiply the variable parts by applying the Product of Powers Rule to each variable with a common base.