Multiply polynomial $ \, \color{blue}{ 3x^2+4x-3 } \, $ by $ \, \color{orangered}{ 8x+5 }$.

$$ \left( \color{blue}{3x^2+4x-3} \right) \cdot \left( \color{orangered}{8x+5} \right) = 24x^3+47x^2-4x-15 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-3} \\ \hline \color{blue}{8x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-3} \\ \hline \color{blue}{8x} & \color{orangered}{24x^3} & \color{orangered}{32x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{5} & \color{orangered}{15x^2} & \color{orangered}{20x} & \color{orangered}{-15} \\ \hline \end{darray} $$

Combine like terms:

$$ 24x^3 + 32x^2 + 15x^2-24x + 20x-15 = \\ 24x^3+47x^2-4x-15 $$

Polynomial Operations Calculator