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.


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


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

Now let’s do this same multiplication using the Vertical Method.


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


try it

Watch the following video to see more examples of multiplying polynomials.