Multiply polynomial $ \, \color{blue}{ 16i^2-16i+16 } \, $ by $ \, \color{orangered}{ 4-4i }$.

$$ \left( \color{blue}{16i^2-16i+16} \right) \cdot \left( \color{orangered}{4-4i} \right) = -64i^3+128i^2-128i+64 $$

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

$$ \begin{aligned} P(x) &= 16i^2-16i+16 \\ Q(x) &= -4i+4 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{16i^2} & \color{blue}{-16i} & \color{blue}{16} \\ \hline \color{blue}{-4i} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{16i^2} & \color{blue}{-16i} & \color{blue}{16} \\ \hline \color{blue}{-4i} & \color{orangered}{-64i^3} & \color{orangered}{64i^2} & \color{orangered}{-64i} \\ \hline \color{blue}{4} & \color{orangered}{64i^2} & \color{orangered}{-64i} & \color{orangered}{64} \\ \hline \end{darray} $$

Combine like terms:

$$ -64i^3 + 64i^2 + 64i^2-64i-64i + 64 = \\ -64i^3+128i^2-128i+64 $$

Polynomial Operations Calculator