Multiplying polynomials by monomials is an application of the distributive property. You know that 3(2x + 5) = 3(2x) + 3(5) = 6x + 15. You also know that (3x)(2x) = 6x2. Using these principles together reveals that 3x(2x + 5) = (3x)(2x) + (3x)(5) = 6x2 + 15x. Extending the distributive property allows you to expand 3x(7x2 + 2x + 5) = (3x)(7x2) + (3x)(2x) + (3x)(5) = 21x3 + 6x2 + 15x.

The distributive property can also be used with multiple variables.