Multiplying Monomials by Polynomials

Example 1

Multiply \(\begin{align*}-2a^2b^4(3ab^2+7a^3b-9a+3)\end{align*}\).

Multiply the monomial by each term inside the parenthesis:

\(\begin{align*}& -2a^2b^4(3ab^2+7a^3b-9a+3)\\ & = (-2a^2b^4)(3ab^2)+(-2a^2b^4)(7a^3b)+(-2a^2b^4)(-9a)+(-2a^2b^4)(3)\\ & = -6a^3b^6-14a^5b^5+18a^5b^4-6a^2b^4\end{align*}\)