Multiplying a monomial into a binomial or other polynomial is a lot like distribution. All of the factors of the monomial are multiplied into each term of the polynomial. Before we complicate things with several variables and exponents, let's briefly review a distribution example.
Monomial Multiplied by a Monomial
When we multiply two terms that contain different coefficients, variables, and powers, we need to make sure that all coefficients are multiplied together, and if the variables are the same, we can increase the exponent power. If variables are not the same, we just write them next to each other to show they have been multiplied. Here are some examples:
Multiplying a Monomial by Binomial
Finally, let's see how we can use the distribute rule and our process for multiplying coefficients and variables with a more complicated example: