Multiplying Two Binomials Using the Distributive Property
Learning Outcomes
- Use the distributive property to multiply two binomials
Using the Distributive Property
We will start by using the Distributive Property. Look again at the following example.We distributed the [latex]p[/latex] to get | [latex]x\color{red}{p}+3\color{red}{p}[/latex] |
What if we have [latex]\left(x+7\right)[/latex] instead of [latex]p[/latex] ? | |
Distribute [latex]\left(x+7\right)[/latex] . | |
Distribute again. | [latex]{x}^{2}+7x+3x+21[/latex] |
Combine like terms. | [latex]{x}^{2}+10x+21[/latex] |
example
Multiply: [latex]\left(x+6\right)\left(x+8\right)[/latex]. Solution[latex]\left(x+6\right)\left(x+8\right)[/latex] | |
Distribute [latex]\left(x+8\right)[/latex] . | [latex]x\color{red}{(x+8)}+6\color{red}{(x+8)}[/latex] |
Distribute again. | [latex]{x}^{2}+8x+6x+48[/latex] |
Simplify. | [latex]{x}^{2}+14x+48[/latex] |
try it
[ohm_question]146207[/ohm_question]example
Multiply: [latex]\left(2x+9\right)\left(3x+4\right)[/latex].Answer: Solution
[latex]\left(2x+9\right)\left(3x+4\right)[/latex] | |
Distribute. [latex]\left(3x+4\right)[/latex] | [latex]2x\color{red}{(3x+4)}+9\color{red}{(3x+4)}[/latex] |
Distribute again. | [latex]6{x}^{2}+8x+27x+36[/latex] |
Simplify. | [latex]6{x}^{2}+35x+36[/latex] |
try it
[ohm_question]146208[/ohm_question]example
Multiply: [latex]\left(4y+3\right)\left(6y - 5\right)[/latex].Answer: Solution
[latex]\left(4y+3\right)\left(6y - 5\right)[/latex] | |
Distribute. | [latex]4y\color{red}{(6y-5)}+3\color{red}{(6y-5)}[/latex] |
Distribute again. | [latex]24{y}^{2}-20y+18y - 15[/latex] |
Simplify. | [latex]24{y}^{2}-2y - 15[/latex] |
try it
[ohm_question]146209[/ohm_question]example
Multiply: [latex]\left(x+2\right)\left(x-y\right)[/latex].Answer: Solution
[latex](x+2)(x-y)[/latex] | |
Distribute. | [latex]x\color{red}{(x-y)}+2\color{red}{(x-y)}[/latex] |
Distribute again. | [latex]x^2-xy+2x-2y[/latex] |
Simplify. | There are no like terms to combine. |
try it
[ohm_question]146210[/ohm_question]Licenses & Attributions
CC licensed content, Original
- Question ID 146210, 146209, 146208, 146207. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Multiply Binomials Using An Area Model and Using Repeated Distribution. Authored by: James Sousa (mathispower4u.com). 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/[email protected].