Multiply polynomial $ \, \color{blue}{ 4a+2 } \, $ by $ \, \color{orangered}{ 6a^2-a+2 }$.

$$ \left( \color{blue}{4a+2} \right) \cdot \left( \color{orangered}{6a^2-a+2} \right) = 24a^3+8a^2+6a+4 $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6a^2} & \color{blue}{-a} & \color{blue}{2} \\ \hline \color{blue}{4a} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6a^2} & \color{blue}{-a} & \color{blue}{2} \\ \hline \color{blue}{4a} & \color{orangered}{24a^3} & \color{orangered}{-4a^2} & \color{orangered}{8a} \\ \hline \color{blue}{2} & \color{orangered}{12a^2} & \color{orangered}{-2a} & \color{orangered}{4} \\ \hline \end{darray} $$

Combine like terms:

$$ 24a^3-4a^2 + 12a^2 + 8a-2a + 4 = \\ 24a^3+8a^2+6a+4 $$

Polynomial Operations Calculator