Multiply polynomial $ \, \color{blue}{ 8x^2-3x+1 } \, $ by $ \, \color{orangered}{ -3x+2 }$.

$$ \left( \color{blue}{8x^2-3x+1} \right) \cdot \left( \color{orangered}{-3x+2} \right) = -24x^3+25x^2-9x+2 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^2} & \color{blue}{-3x} & \color{blue}{1} \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^2} & \color{blue}{-3x} & \color{blue}{1} \\ \hline \color{blue}{-3x} & \color{orangered}{-24x^3} & \color{orangered}{9x^2} & \color{orangered}{-3x} \\ \hline \color{blue}{2} & \color{orangered}{16x^2} & \color{orangered}{-6x} & \color{orangered}{2} \\ \hline \end{darray} $$

Combine like terms:

$$ -24x^3 + 9x^2 + 16x^2-3x-6x + 2 = \\ -24x^3+25x^2-9x+2 $$

Polynomial Operations Calculator