Question
Multiply polynomial $ \, \color{blue}{ x^2-4x-4 } \, $ by $ \, \color{orangered}{ 4x+5 }$.
Answer
$$ \left( \color{blue}{x^2-4x-4} \right) \cdot \left( \color{orangered}{4x+5} \right) = 4x^3-11x^2-36x-20 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-4x} & \color{blue}{-4} \\ \hline \color{blue}{4x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-4x} & \color{blue}{-4} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{-16x^2} & \color{orangered}{-16x} \\ \hline \color{blue}{5} & \color{orangered}{5x^2} & \color{orangered}{-20x} & \color{orangered}{-20} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^3-16x^2 + 5x^2-16x-20x-20 = \\ 4x^3-11x^2-36x-20 $$This page was created using
Polynomial Operations Calculator