Multiply polynomial $ \, \color{blue}{ x^2+12x+32 } \, $ by $ \, \color{orangered}{ x+4 }$.

$$ \left( \color{blue}{x^2+12x+32} \right) \cdot \left( \color{orangered}{x+4} \right) = x^3+16x^2+80x+128 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{12x} & \color{blue}{32} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{12x} & \color{blue}{32} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{12x^2} & \color{orangered}{32x} \\ \hline \color{blue}{4} & \color{orangered}{4x^2} & \color{orangered}{48x} & \color{orangered}{128} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3 + 12x^2 + 4x^2 + 32x + 48x + 128 = \\ x^3+16x^2+80x+128 $$

Polynomial Operations Calculator