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.
Candela Citations
CC licensed content, Original
- Question ID 146218, 146217. Authored by: Question ID 146218, 146217. Provided by: Lumen Learning. License: CC BY: Attribution
CC licensed content, Shared previously
- Ex: Polynomial Multiplication Involving Binomials and Trinomials. Authored by: Lumen Learning. Located at: https://youtu.be/bBKbldmlbqI. License: CC BY: Attribution
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax. License: CC BY: Attribution. License Terms: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757