Subtract polynomials: $ \, \color{blue}{ 7x^4-5x^3+8x^2+9x-13 } \, $ , $ \, \color{orangered}{ 2x^4+6x^3-4x^2-x+4 }$.

$$ \left( \color{blue}{7x^4-5x^3+8x^2+9x-13} \right) - \left( \color{orangered}{2x^4+6x^3-4x^2-x+4} \right) = 5x^4-11x^3+12x^2+10x-17 $$

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

$$ \begin{array}{lrrrrr} & 7x^4 & -5x^3 & 8x^2 & 9x & -13 \\ \color{red}{ - } & 2x^4 & 6x^3 & -4x^2 & -x & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 7x^4 & -5x^3 & 8x^2 & 9x & -13 \\ \color{red}{ - } & -2x^4 & -6x^3 & 4x^2 & x & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 7x^4 & -5x^3 & 8x^2 & 9x & -13 \\ \color{red}{ - } & -2x^4 & -6x^3 & 4x^2 & x & -4 \\ \hline & 9x^4 & x^3 & 4x^2 & 8x & -9 \end{array} $$

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