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