Question
Multiply polynomial $ \, \color{blue}{ 4x-2 } \, $ by $ \, \color{orangered}{ -4x^2-x+1 }$.
Answer
$$ \left( \color{blue}{4x-2} \right) \cdot \left( \color{orangered}{-4x^2-x+1} \right) = -16x^3+4x^2+6x-2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-x} & \color{blue}{1} \\ \hline \color{blue}{4x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-x} & \color{blue}{1} \\ \hline \color{blue}{4x} & \color{orangered}{-16x^3} & \color{orangered}{-4x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-2} & \color{orangered}{8x^2} & \color{orangered}{2x} & \color{orangered}{-2} \\ \hline \end{darray} $$Combine like terms:
$$ -16x^3-4x^2 + 8x^2 + 4x + 2x-2 = \\ -16x^3+4x^2+6x-2 $$This page was created using
Polynomial Operations Calculator