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

$$ \begin{aligned} P(x) &= -4x+2 \\ Q(x) &= 4x^2+4x+1 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{4x} & \color{blue}{1} \\ \hline \color{blue}{-4x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{4x} & \color{blue}{1} \\ \hline \color{blue}{-4x} & \color{orangered}{-16x^3} & \color{orangered}{-16x^2} & \color{orangered}{-4x} \\ \hline \color{blue}{2} & \color{orangered}{8x^2} & \color{orangered}{8x} & \color{orangered}{2} \\ \hline \end{darray} $$

Combine like terms:

$$ -16x^3-16x^2 + 8x^2-4x + 8x + 2 = \\ -16x^3-8x^2+4x+2 $$

Polynomial Operations Calculator