Multiplying a Polynomial by a Monomial

Learning Outcomes

• Multiply a polynomial by a monomial using the distributive property

Previously, you learned to use the Distributive Property to simplify expressions such as $2\left(x - 3\right)$. You multiplied both terms in the parentheses, $x\text{ and }3$, by $2$, to get $2x - 6$. With this chapter’s new vocabulary, you can say you were multiplying a binomial, $x - 3$, by a monomial, $2$. Multiplying a binomial by a monomial is nothing new for you!

example

Multiply: $3\left(x+7\right)$

Solution

 $3\left(x+7\right)$ Distribute. $3\cdot x+3\cdot 7$ Simplify. $3x+21$

example

Multiply: $x\left(x - 8\right)$

example

Multiply: $10x\left(4x+y\right)$

try it

Multiplying a monomial by a trinomial works in much the same way.

example

Multiply: $-2x\left(5{x}^{2}+7x - 3\right)$

example

Multiply: $4{y}^{3}\left({y}^{2}-8y+1\right)$

try it

Now we will have the monomial as the second factor.

example

Multiply: $\left(x+3\right)p$

try it

In the following video we show more examples of how to multiply monomials with other polynomials.