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

$$ \begin{aligned} P(x) &= 8n^2-3n+6 \\ Q(x) &= 7n^3-3n^2-1 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8n^2} & \color{blue}{-3n} & \color{blue}{6} \\ \hline \color{blue}{7n^3} & & & \\ \hline \color{blue}{-3n^2} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8n^2} & \color{blue}{-3n} & \color{blue}{6} \\ \hline \color{blue}{7n^3} & \color{orangered}{56n^5} & \color{orangered}{-21n^4} & \color{orangered}{42n^3} \\ \hline \color{blue}{-3n^2} & \color{orangered}{-24n^4} & \color{orangered}{9n^3} & \color{orangered}{-18n^2} \\ \hline \color{blue}{-1} & \color{orangered}{-8n^2} & \color{orangered}{3n} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ 56n^5-21n^4-24n^4 + 42n^3 + 9n^3-8n^2-18n^2 + 3n-6 = \\ 56n^5-45n^4+51n^3-26n^2+3n-6 $$

Polynomial Operations Calculator