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

$$ \left( \color{blue}{16-16i+16i^2} \right) \cdot \left( \color{orangered}{16-16i+16i^2} \right) = 256i^4-512i^3+768i^2-512i+256 $$

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

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

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{16i^2} & \color{blue}{-16i} & \color{blue}{16} \\ \hline \color{blue}{16i^2} & \color{orangered}{256i^4} & \color{orangered}{-256i^3} & \color{orangered}{256i^2} \\ \hline \color{blue}{-16i} & \color{orangered}{-256i^3} & \color{orangered}{256i^2} & \color{orangered}{-256i} \\ \hline \color{blue}{16} & \color{orangered}{256i^2} & \color{orangered}{-256i} & \color{orangered}{256} \\ \hline \end{darray} $$

Combine like terms:

$$ 256i^4-256i^3-256i^3 + 256i^2 + 256i^2 + 256i^2-256i-256i + 256 = \\ 256i^4-512i^3+768i^2-512i+256 $$

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