# Multiplying Polynomials by Monomials

Multiplying polynomials by monomials is an application of the distributive property. You know that 3(2*x* + 5) = 3(2*x*) + 3(5) = 6*x* + 15. You also know that (3*x*)(2*x*) = 6*x*2. Using these principles together reveals that 3*x*(2*x* + 5) = (3*x*)(2*x*) + (3*x*)(5) = 6*x*2 + 15*x*. Extending the distributive property allows you to expand 3*x*(7*x*2 + 2*x* + 5) = (3*x*)(7*x*2) + (3*x*)(2*x*) + (3*x*)(5) = 21*x*3 + 6*x*2 + 15*x*.

The distributive property can also be used with multiple variables.