Multiply polynomial $ \, \color{blue}{ 3x^2-6x+4 } \, $ by $ \, \color{orangered}{ 7x-1 }$.

$$ \left( \color{blue}{3x^2-6x+4} \right) \cdot \left( \color{orangered}{7x-1} \right) = 21x^3-45x^2+34x-4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{7x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{7x} & \color{orangered}{21x^3} & \color{orangered}{-42x^2} & \color{orangered}{28x} \\ \hline \color{blue}{-1} & \color{orangered}{-3x^2} & \color{orangered}{6x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ 21x^3-42x^2-3x^2 + 28x + 6x-4 = \\ 21x^3-45x^2+34x-4 $$

Polynomial Operations Calculator