Performing Operations with Polynomials of Several Variables
We have looked at polynomials containing only one variable. However, a polynomial can contain several variables. All of the same rules apply when working with polynomials containing several variables. Consider an example:[latex]\begin{array}{cc}\left(a+2b\right)\left(4a-b-c\right)\hfill & \hfill \\ a\left(4a-b-c\right)+2b\left(4a-b-c\right)\hfill & \text{Use the distributive property}.\hfill \\ 4{a}^{2}-ab-ac+8ab - 2{b}^{2}-2bc\hfill & \text{Multiply}.\hfill \\ 4{a}^{2}+\left(-ab+8ab\right)-ac - 2{b}^{2}-2bc\hfill & \text{Combine like terms}.\hfill \\ 4{a}^{2}+7ab-ac - 2bc - 2{b}^{2}\hfill & \text{Simplify}.\hfill \end{array}[/latex]
Example 8: Multiplying Polynomials Containing Several Variables
Multiply [latex]\left(x+4\right)\left(3x - 2y+5\right)[/latex].Solution
Follow the same steps that we used to multiply polynomials containing only one variable.[latex]\begin{array}{cc}x\left(3x - 2y+5\right)+4\left(3x - 2y+5\right) \hfill & \text{Use the distributive property}.\hfill \\ 3{x}^{2}-2xy+5x+12x - 8y+20\hfill & \text{Multiply}.\hfill \\ 3{x}^{2}-2xy+\left(5x+12x\right)-8y+20\hfill & \text{Combine like terms}.\hfill \\ 3{x}^{2}-2xy+17x - 8y+20 \hfill & \text{Simplify}.\hfill \end{array}[/latex]
Try It 8
[latex]\left(3x - 1\right)\left(2x+7y - 9\right)[/latex]. SolutionLicenses & Attributions
CC licensed content, Specific attribution
- College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.
