Question
Multiply polynomial $ \, \color{blue}{ 8a-2 } \, $ by $ \, \color{orangered}{ 3a^2+2a-2 }$.
Answer
$$ \left( \color{blue}{8a-2} \right) \cdot \left( \color{orangered}{3a^2+2a-2} \right) = 24a^3+10a^2-20a+4 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3a^2} & \color{blue}{2a} & \color{blue}{-2} \\ \hline \color{blue}{8a} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3a^2} & \color{blue}{2a} & \color{blue}{-2} \\ \hline \color{blue}{8a} & \color{orangered}{24a^3} & \color{orangered}{16a^2} & \color{orangered}{-16a} \\ \hline \color{blue}{-2} & \color{orangered}{-6a^2} & \color{orangered}{-4a} & \color{orangered}{4} \\ \hline \end{darray} $$Combine like terms:
$$ 24a^3 + 16a^2-6a^2-16a-4a + 4 = \\ 24a^3+10a^2-20a+4 $$This page was created using
Polynomial Operations Calculator