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