# What is Multiplication of Monomials by Polynomials?

It works the same as with numbers. For numbers, you know that $a \left(b + c\right)$ equals $a b + a c$.
For example, if your monomial is $3 {x}^{2}$, and your polynomial is $3 + 2 x - 5 {x}^{2} + 8 {x}^{3}$, the product is
$3 {x}^{2} \left(3 + 2 x - 5 {x}^{2} + 8 {x}^{3}\right)$
$3 {x}^{2} \setminus \cdot 3 + 3 {x}^{2} \setminus \cdot 2 x - 3 {x}^{2} \setminus \cdot 5 {x}^{2} + 3 {x}^{2} \setminus \cdot 8 {x}^{3}$, which is
$9 {x}^{2} + 6 {x}^{3} - 15 {x}^{4} + 24 {x}^{5}$