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]

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]

Show Solution

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]

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