Subtract polynomials: $ \, \color{blue}{ -2x^6+x^5-3x^2-4x+7 } \, $ , $ \, \color{orangered}{ x^5+2x^2-4x+4 }$.

$$ \left( \color{blue}{-2x^6+x^5-3x^2-4x+7} \right) - \left( \color{orangered}{x^5+2x^2-4x+4} \right) = -2x^6-5x^2+3 $$

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

$$ \begin{array}{lrrrrr} & -2x^6 & x^5 & -3x^2 & -4x & 7 \\ \color{red}{ - } & & x^5 & 2x^2 & -4x & 4 \\ \hline \end{array} $$

Step 2: Change ALL the signs in the second row.

$$ \begin{array}{lrrrrr} & -2x^6 & x^5 & -3x^2 & -4x & 7 \\ \color{red}{ - } & & -x^5 & -2x^2 & 4x & -4 \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrrrr} & -2x^6 & x^5 & -3x^2 & -4x & 7 \\ \color{red}{ - } & & -x^5 & -2x^2 & 4x & -4 \\ \hline & -2x^6 & 2x^5 & -x^2 & -8x & 11 \end{array} $$

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