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

$$ \left( \color{blue}{4b^2-2} \right) \cdot \left( \color{orangered}{4b^2+2-2b} \right) = 16b^4-8b^3+4b-4 $$

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

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

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

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

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