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

$$ \left( \color{blue}{x^4+8x^3+9x^2} \right) - \left( \color{orangered}{5x^4+4x^3+2x^2} \right) = -4x^4+4x^3+7x^2 $$

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

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

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

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

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

$$ \begin{array}{lrrr} & x^4 & 8x^3 & 9x^2 \\ \color{red}{ - } & -5x^4 & -4x^3 & -2x^2 \\ \hline & 6x^4 & 12x^3 & 11x^2 \end{array} $$

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