Vertical and FOIL Methods for Multiplying Two Binomials
Learning Outcomes
- Use the FOIL method to multiply two binomials
- Use the vertical method to multiply two binomials
example
Multiply using the FOIL method: [latex]\left(x+6\right)\left(x+9\right)[/latex]. SolutionStep 1: Multiply the First terms. | |
Step 2: Multiply the Outer terms. | |
Step 3: Multiply the Inner terms. | |
Step 4: Multiply the Last terms. | |
Step 5: Combine like terms, when possible. | [latex]x^2+15x+54[/latex] |
try it
[ohm_question]146211[/ohm_question]Use the FOIL method for multiplying two binomials
- Multiply the First terms.
- Multiply the Outer terms.
- Multiply the Inner terms.
- Multiply the Last terms.
- Combine like terms, when possible.
example
Multiply: [latex]\left(y - 8\right)\left(y+6\right)[/latex].Answer: Solution
Step 1: Multiply the First terms. | |
Step 2: Multiply the Outer terms. | |
Step 3: Multiply the Inner terms. | |
Step 4: Multiply the Last terms. | |
Step 5: Combine like terms | [latex]y^2-2y-48[/latex] |
try it
[ohm_question]146212[/ohm_question]example
Multiply: [latex]\left(2a+3\right)\left(3a - 1\right)[/latex].Answer: Solution
[latex](2a+3)(3a-1)[/latex] | |
Multiply the First terms. | |
Multiply the Outer terms. | |
Multiply the Inner terms. | |
Multiply the Last terms. | |
Combine like terms. | [latex]6a^2+7a-3[/latex] |
try it
[ohm_question]146213[/ohm_question]example
Multiply: [latex]\left(5x-y\right)\left(2x - 7\right)[/latex].Answer: Solution
[latex](5x-y)(2x-7)[/latex] | |
Multiply the First terms. | |
Multiply the Outer terms. | |
Multiply the Inner terms. | |
Multiply the Last terms. | |
Combine like terms. There are none. | [latex]10x^2-35x-2xy\color{red}{+7y}[/latex] |
try it
[ohm_question]146215[/ohm_question]Multiplying Two Binomials Using the Vertical Method
The FOIL method is usually the quickest method for multiplying two binomials, but it works only for binomials. You can use the Distributive Property to find the product of any two polynomials. Another method that works for all polynomials is the Vertical Method. It is very much like the method you use to multiply whole numbers. Look carefully at this example of multiplying two-digit numbers. You start by multiplying [latex]23[/latex] by [latex]6[/latex] to get [latex]138[/latex]. Then you multiply [latex]23[/latex] by [latex]4[/latex], lining up the partial product in the correct columns. Last, you add the partial products. Now we'll apply this same method to multiply two binomials.example
Multiply using the vertical method: [latex]\left(5x - 1\right)\left(2x - 7\right)[/latex]. Solution It does not matter which binomial goes on the top. Line up the columns when you multiply as we did when we multiplied [latex]23\left(46\right)[/latex].Multiply [latex]2x - 7[/latex] by [latex]-1[/latex] . | |
Multiply [latex]2x - 7[/latex] by [latex]5x[/latex] . | |
Add like terms. |
try it
[ohm_question]146216[/ohm_question]Multiplying Two Binomials
To multiply binomials, use the:- Distributive Property
- FOIL Method
- Vertical Method
Licenses & Attributions
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- Question ID 146215, 146213, 146212, 146211. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Find The Product of Two Binomials (09x-52). Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.
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- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].