Multiply polynomial $ \, \color{blue}{ 2x^2-5x+6 } \, $ by $ \, \color{orangered}{ 3x-2 }$.

$$ \left( \color{blue}{2x^2-5x+6} \right) \cdot \left( \color{orangered}{3x-2} \right) = 6x^3-19x^2+28x-12 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{-15x^2} & \color{orangered}{18x} \\ \hline \color{blue}{-2} & \color{orangered}{-4x^2} & \color{orangered}{10x} & \color{orangered}{-12} \\ \hline \end{darray} $$

Combine like terms:

$$ 6x^3-15x^2-4x^2 + 18x + 10x-12 = \\ 6x^3-19x^2+28x-12 $$

Polynomial Operations Calculator