Question
Multiply polynomial $ \, \color{blue}{ 8a-6 } \, $ by $ \, \color{orangered}{ 2a^2+3a+2 }$.
Answer
$$ \left( \color{blue}{8a-6} \right) \cdot \left( \color{orangered}{2a^2+3a+2} \right) = 16a^3+12a^2-2a-12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2a^2} & \color{blue}{3a} & \color{blue}{2} \\ \hline \color{blue}{8a} & & & \\ \hline \color{blue}{-6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2a^2} & \color{blue}{3a} & \color{blue}{2} \\ \hline \color{blue}{8a} & \color{orangered}{16a^3} & \color{orangered}{24a^2} & \color{orangered}{16a} \\ \hline \color{blue}{-6} & \color{orangered}{-12a^2} & \color{orangered}{-18a} & \color{orangered}{-12} \\ \hline \end{darray} $$Combine like terms:
$$ 16a^3 + 24a^2-12a^2 + 16a-18a-12 = \\ 16a^3+12a^2-2a-12 $$This page was created using
Polynomial Operations Calculator