Question
Multiply polynomial $ \, \color{blue}{ -7x^2+14x-7 } \, $ by $ \, \color{orangered}{ x-2 }$.
Answer
$$ \left( \color{blue}{-7x^2+14x-7} \right) \cdot \left( \color{orangered}{x-2} \right) = -7x^3+28x^2-35x+14 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-7x^2} & \color{blue}{14x} & \color{blue}{-7} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-7x^2} & \color{blue}{14x} & \color{blue}{-7} \\ \hline \color{blue}{x} & \color{orangered}{-7x^3} & \color{orangered}{14x^2} & \color{orangered}{-7x} \\ \hline \color{blue}{-2} & \color{orangered}{14x^2} & \color{orangered}{-28x} & \color{orangered}{14} \\ \hline \end{darray} $$Combine like terms:
$$ -7x^3 + 14x^2 + 14x^2-7x-28x + 14 = \\ -7x^3+28x^2-35x+14 $$This page was created using
Polynomial Operations Calculator