Multiply polynomial $ \, \color{blue}{ 2x-3 } \, $ by $ \, \color{orangered}{ -4x^2-2x+7 }$.

$$ \left( \color{blue}{2x-3} \right) \cdot \left( \color{orangered}{-4x^2-2x+7} \right) = -8x^3+8x^2+20x-21 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-2x} & \color{blue}{7} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-2x} & \color{blue}{7} \\ \hline \color{blue}{2x} & \color{orangered}{-8x^3} & \color{orangered}{-4x^2} & \color{orangered}{14x} \\ \hline \color{blue}{-3} & \color{orangered}{12x^2} & \color{orangered}{6x} & \color{orangered}{-21} \\ \hline \end{darray} $$

Combine like terms:

$$ -8x^3-4x^2 + 12x^2 + 14x + 6x-21 = \\ -8x^3+8x^2+20x-21 $$

Polynomial Operations Calculator