Add $ \, \color{blue}{ x^6+7x^5+2x^4+9x^3+10x^2+12x+15 } \, $ and $ \, \color{orangered}{ x^6+9x^5+8x^4+9x^3+12x^2+15x+20 }$.

$$ \left( \color{blue}{x^6+7x^5+2x^4+9x^3+10x^2+12x+15} \right) + \left( \color{orangered}{x^6+9x^5+8x^4+9x^3+12x^2+15x+20} \right) = 2x^6+16x^5+10x^4+18x^3+22x^2+27x+35 $$

Step 1: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrrrrrr} & x^6 & 7x^5 & 2x^4 & 9x^3 & 10x^2 & 12x & 15 \\ \color{blue}{ + } & x^6 & 9x^5 & 8x^4 & 9x^3 & 12x^2 & 15x & 20 \\ \hline \end{array} $$

Step 2: Combine like terms (add each column):

$$ \begin{array}{lrrrrrrr} & x^6 & 7x^5 & 2x^4 & 9x^3 & 10x^2 & 12x & 15 \\ \color{blue}{ + } & x^6 & 9x^5 & 8x^4 & 9x^3 & 12x^2 & 15x & 20 \\ \hline & 2x^6 & 16x^5 & 10x^4 & 18x^3 & 22x^2 & 27x & 35 \end{array} $$

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