Question
Multiply polynomial $ \, \color{blue}{ 4d-3 } \, $ by $ \, \color{orangered}{ -d^2-d-1 }$.
Answer
$$ \left( \color{blue}{4d-3} \right) \cdot \left( \color{orangered}{-d^2-d-1} \right) = -4d^3-d^2-d+3 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-d^2} & \color{blue}{-d} & \color{blue}{-1} \\ \hline \color{blue}{4d} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-d^2} & \color{blue}{-d} & \color{blue}{-1} \\ \hline \color{blue}{4d} & \color{orangered}{-4d^3} & \color{orangered}{-4d^2} & \color{orangered}{-4d} \\ \hline \color{blue}{-3} & \color{orangered}{3d^2} & \color{orangered}{3d} & \color{orangered}{3} \\ \hline \end{darray} $$Combine like terms:
$$ -4d^3-4d^2 + 3d^2-4d + 3d + 3 = \\ -4d^3-d^2-d+3 $$This page was created using
Polynomial Operations Calculator