Multiply monomials

Learning Objectives Define a monomial and identify its components (coefficient, variable, exponent). Recall and apply the Product of Powers Rule for exponents. Multiply the coefficients of two or more monomials. Combine the variable parts of two or more monomials by adding their exponents. Multiply two or more monomials together to produce a single, simplified monomial. Apply the multiplication of monomials to solve problems involving geometric area. Ever wondered how to find the area of a rectangle whose sides are `3x` and `5x²`? 🤔 Let's unlock the method to solve problems just like this! In this tutorial, you will learn the step-by-step process for multiplying monomials. This is a fundamental skill for working with polynomials, which are the building blocks of the q...

TermDefinitionExample MonomialA single term that is a number, a variable, or a product of a number and one or more variables with non-negative integer exponents. It has no addition or subtraction signs.`7x²y` is a monomial. `7x + y` is not. CoefficientThe numerical factor of a monomial.In the monomial `-5a³`, the coefficient is `-5`. VariableA symbol, usually a letter, used to represent an unknown value.In the monomial `12z`, the variable is `z`. BaseThe number or variable that is being raised to a power.In the term `x⁴`, the base is `x`. Exponent (or Power)A number indicating how many times to multiply the base by itself.In the term `x⁴`, the exponent is `4`. It means `x * x * x * x`.

Product of Powers Rule x^a * x^b = x^{a+b} When multiplying two powers with the same base, you keep the base and add the exponents. Commutative Property of Multiplication a * b = b * a This property allows you to reorder the factors in a multiplication problem. We use it to group coefficients together and like variables together. Associative Property of Multiplication (a * b) * c = a * (b * c) This property allows you to change the grouping of factors. It works with the Commutative Property to let you multiply all the coefficients first, then each variable group.