{"id":292,"date":"2015-09-18T20:39:44","date_gmt":"2015-09-18T20:39:44","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=292"},"modified":"2015-11-03T21:39:58","modified_gmt":"2015-11-03T21:39:58","slug":"performing-operations-with-polynomials-of-several-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/performing-operations-with-polynomials-of-several-variables\/","title":{"raw":"Performing Operations with Polynomials of Several Variables","rendered":"Performing Operations with Polynomials of Several Variables"},"content":{"raw":"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:\r\n
[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]<\/div>\r\n
\r\n

Example 8: Multiplying Polynomials Containing Several Variables<\/h3>\r\nMultiply [latex]\\left(x+4\\right)\\left(3x - 2y+5\\right)[\/latex].\r\n\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\nFollow the same steps that we used to multiply polynomials containing only one variable.\r\n
[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]<\/div>\r\n<\/div>\r\n
\r\n

Try It 8<\/h3>\r\n[latex]\\left(3x - 1\\right)\\left(2x+7y - 9\\right)[\/latex].\r\n\r\nSolution<\/a>\r\n\r\n<\/div>","rendered":"

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:<\/p>\n

[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]<\/div>\n
\n

Example 8: Multiplying Polynomials Containing Several Variables<\/h3>\n

Multiply [latex]\\left(x+4\\right)\\left(3x - 2y+5\\right)[\/latex].<\/p>\n<\/div>\n

\n

Solution<\/h3>\n

Follow the same steps that we used to multiply polynomials containing only one variable.<\/p>\n

[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]<\/div>\n<\/div>\n
\n

Try It 8<\/h3>\n

[latex]\\left(3x - 1\\right)\\left(2x+7y - 9\\right)[\/latex].<\/p>\n

Solution<\/a><\/p>\n<\/div>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\t
CC licensed content, Specific attribution<\/div>