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

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

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4c^4} & \color{blue}{2c^2} & \color{blue}{4} \\ \hline \color{blue}{-3c^2} & & & \\ \hline \color{blue}{-3c} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4c^4} & \color{blue}{2c^2} & \color{blue}{4} \\ \hline \color{blue}{-3c^2} & \color{orangered}{12c^6} & \color{orangered}{-6c^4} & \color{orangered}{-12c^2} \\ \hline \color{blue}{-3c} & \color{orangered}{12c^5} & \color{orangered}{-6c^3} & \color{orangered}{-12c} \\ \hline \end{darray} $$

Combine like terms:

$$ 12c^6-6c^4 + 12c^5-12c^2-6c^3-12c = \\ 12c^6+12c^5-6c^4-6c^3-12c^2-12c $$

Polynomial Operations Calculator