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

$$ \left( \color{blue}{x^2+6x-4} \right) \cdot \left( \color{orangered}{2x-4} \right) = 2x^3+8x^2-32x+16 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{6x} & \color{blue}{-4} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{12x^2} & \color{orangered}{-8x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{-24x} & \color{orangered}{16} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3 + 12x^2-4x^2-8x-24x + 16 = \\ 2x^3+8x^2-32x+16 $$

Polynomial Operations Calculator