Subtract polynomials: $ \, \color{blue}{ 8n^3+6n^2+n-7 } \, $ , $ \, \color{orangered}{ \cancel{8n}-2n^2 -\cancel{8n} }$.

$$ \left( \color{blue}{8n^3+6n^2+n-7} \right) - \left( \color{orangered}{ \cancel{8n}-2n^2 -\cancel{8n}} \right) = 8n^3+8n^2+n-7 $$

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

$$ \begin{aligned} P(x) &= 8n^3+6n^2+n-7 \\ Q(x) &= -2n^2 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 8n^3 & 6n^2 & n & -7 \\ \color{red}{ - } & & -2n^2 & & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 8n^3 & 6n^2 & n & -7 \\ \color{red}{ - } & & 2n^2 & & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 8n^3 & 6n^2 & n & -7 \\ \color{red}{ - } & & 2n^2 & & \\ \hline & 8n^3 & 4n^2 & n & -7 \end{array} $$

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