Question
Multiply polynomial $ \, \color{blue}{ 3c+2 } \, $ by $ \, \color{orangered}{ c^2-6c-4 }$.
Answer
$$ \left( \color{blue}{3c+2} \right) \cdot \left( \color{orangered}{c^2-6c-4} \right) = 3c^3-16c^2-24c-8 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{c^2} & \color{blue}{-6c} & \color{blue}{-4} \\ \hline \color{blue}{3c} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{c^2} & \color{blue}{-6c} & \color{blue}{-4} \\ \hline \color{blue}{3c} & \color{orangered}{3c^3} & \color{orangered}{-18c^2} & \color{orangered}{-12c} \\ \hline \color{blue}{2} & \color{orangered}{2c^2} & \color{orangered}{-12c} & \color{orangered}{-8} \\ \hline \end{darray} $$Combine like terms:
$$ 3c^3-18c^2 + 2c^2-12c-12c-8 = \\ 3c^3-16c^2-24c-8 $$This page was created using
Polynomial Operations Calculator