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 [latex]2\left(x - 3\right)[/latex]. You multiplied both terms in the parentheses, [latex]x\text{ and }3[/latex], by [latex]2[/latex], to get [latex]2x - 6[/latex]. With this chapter’s new vocabulary, you can say you were multiplying a binomial, [latex]x - 3[/latex], by a monomial, [latex]2[/latex]. Multiplying a binomial by a monomial is nothing new for you!

example

Multiply: [latex]3\left(x+7\right)[/latex]

Solution

[latex]3\left(x+7\right)[/latex]
Distribute. .
[latex]3\cdot x+3\cdot 7[/latex]
Simplify. [latex]3x+21[/latex]

 

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example

Multiply: [latex]x\left(x - 8\right)[/latex]

 

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example

Multiply: [latex]10x\left(4x+y\right)[/latex]

 

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

example

Multiply: [latex]-2x\left(5{x}^{2}+7x - 3\right)[/latex]

 

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example

Multiply: [latex]4{y}^{3}\left({y}^{2}-8y+1\right)[/latex]

 

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Now we will have the monomial as the second factor.

example

Multiply: [latex]\left(x+3\right)p[/latex]

 

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