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Color this Polynomial Simplified A visualization method for simplifying expressions. A GEMS Submission/ALEX Submitted by: E. Thompson, PhD. Summer 2008

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Why this method works: Helps organize like terms Eliminates overlooking a term Keeps everything from running together Can be used on a problem with any level of difficultyCan be used on a problem with any level of difficulty Can be re-visited with solving equations

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Use color to change the way you visualize the problem: 2x – 3y +2x 2 – 6x +9y - Original Problem 2x – 3y +2x 2 – 6x +9y - Find all xs 2x – 3y +2x 2 – 6x +9y - Find all ys 2x – 3y +2x 2 – 6x +9y - Find all x 2 -4x +6y +2x 2 - Combine like terms +2x 2 -4x +6y – Highest power in front Final Answer: 2x 2 -4x +6y

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The simple process Go through the problem and highlight things that are alike.

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Variation with shapes: (Colors not required) 2x – 3y +2x 2 – 6x +9y - Original Problem 2x – 3y +2x 2 – 6x +9y - Find all xs 2x – 3y +2x 2 – 6x +9y - Find all ys 2x – 3y +2x 2 – 6x +9y - Find all x 2 -4x +6y +2x 2 - Combine like terms +2x 2 -4x +6y – Highest power in front Final Answer: 2x 2 -4x +6y

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Increased Difficulty 2(x – y)+ 2y-3x +x 2 y Original Problem 2(x – y)+ 2y -3x +x 2 y Remove Parenthesis 2x –2y + 2y -3x +x 2 y Group with color -x + 0y +x 2 y Simplify -x +x 2 y Regroup x 2 y -x Final Answer Continue with class samples and individual practice.

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Distribute by multiplication: 15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what.

Distribute by multiplication: 15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what.

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