## Multiplying a Polynomial By a Monomial

Contents

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. |