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

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

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 6k^3+k^2-4 \\ Q(x) &= 5k^3-3k^2+7k \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

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

Step 3: Change ALL the signs in the second row.

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

Step 4: Combine like terms (add each column):

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

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