Mathematics » Polynomials II » Multiply Polynomials

# Multiplying a Polynomial By a Monomial

## Multiplying a Polynomial By a Monomial

We have used the Distributive Property to simplify expressions like $$2\left(x-3\right)$$. You multiplied both terms in the parentheses, $$x\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}3$$, by 2, to get $$2x-6$$. With this tutorial’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! Here’s an example:

## Example

Multiply: $$4\left(x+3\right).$$

### Solution

 Distribute. Simplify.

## Example

Multiply: $$y\left(y-2\right).$$

### Solution

 Distribute. Simplify.

## Example

Multiply: $$7x\left(2x+y\right).$$

### Solution

 Distribute. Simplify.

## Example

Multiply: $$-2y\left(4{y}^{2}+3y-5\right).$$

### Solution

 Distribute. Simplify.

## Example

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

### Solution

 Distribute. Simplify.

## Example

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

### Solution

 The monomial is the second factor. Distribute. Simplify.

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