Question
Multiply polynomial $ \, \color{blue}{ 4s+4 } \, $ by $ \, \color{orangered}{ s^2-4s+4 }$.
Answer
$$ \left( \color{blue}{4s+4} \right) \cdot \left( \color{orangered}{s^2-4s+4} \right) = 4s^3-12s^2+16 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{s^2} & \color{blue}{-4s} & \color{blue}{4} \\ \hline \color{blue}{4s} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{s^2} & \color{blue}{-4s} & \color{blue}{4} \\ \hline \color{blue}{4s} & \color{orangered}{4s^3} & \color{orangered}{-16s^2} & \color{orangered}{16s} \\ \hline \color{blue}{4} & \color{orangered}{4s^2} & \color{orangered}{-16s} & \color{orangered}{16} \\ \hline \end{darray} $$Combine like terms:
$$ 4s^3-16s^2 + 4s^2 + 16s-16s + 16 = \\ 4s^3-12s^2+16 $$This page was created using
Polynomial Operations Calculator