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Study Guides > Prealgebra

Multiplying a Trinomial By a Binomial

Learning Outcomes

  • Multiply a trinomial by a binomial
  We have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we're ready to multiply a trinomial by a binomial. Remember, the FOIL method will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.  

example

Multiply using the Distributive Property: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex]. Solution
.
Distribute. [latex]x\color{red}{(2x^2-5x+8)}+3\color{red}{(2x^2-5x+8)}[/latex]
Multiply. [latex]2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24[/latex]
Combine like terms. [latex]2{x}^{3}+{x}^{2}-7x+24[/latex]
 

try it

[ohm_question]146217[/ohm_question]
  Now let's do this same multiplication using the Vertical Method.  

example

Multiply using the Vertical Method: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex].

Answer: Solution It is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.

.
Multiply [latex]\left(2{x}^{2}-5x+8\right)[/latex] by [latex]3[/latex]. [latex]6x^2-15x+24[/latex]
Multiply [latex]\left(2{x}^{2}-5x+8\right)[/latex] by [latex]x[/latex] . [latex]2x^3-5x^2+8x[/latex]
Add like terms. [latex]2x^3+x^2-7x+24[/latex]

 

try it

[ohm_question]146218[/ohm_question]
  Watch the following video to see more examples of multiplying polynomials. https://youtu.be/bBKbldmlbqI

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  • Ex: Polynomial Multiplication Involving Binomials and Trinomials. Authored by: Lumen Learning. License: CC BY: Attribution.

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