Question
Multiply polynomial $ \, \color{blue}{ 4b-4 } \, $ by $ \, \color{orangered}{ 4b^2+3b-3 }$.
Answer
$$ \left( \color{blue}{4b-4} \right) \cdot \left( \color{orangered}{4b^2+3b-3} \right) = 16b^3-4b^2-24b+12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4b^2} & \color{blue}{3b} & \color{blue}{-3} \\ \hline \color{blue}{4b} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4b^2} & \color{blue}{3b} & \color{blue}{-3} \\ \hline \color{blue}{4b} & \color{orangered}{16b^3} & \color{orangered}{12b^2} & \color{orangered}{-12b} \\ \hline \color{blue}{-4} & \color{orangered}{-16b^2} & \color{orangered}{-12b} & \color{orangered}{12} \\ \hline \end{darray} $$Combine like terms:
$$ 16b^3 + 12b^2-16b^2-12b-12b + 12 = \\ 16b^3-4b^2-24b+12 $$This page was created using
Polynomial Operations Calculator