Question
Multiply polynomial $ \, \color{blue}{ -2x^2-5x+7 } \, $ by $ \, \color{orangered}{ -2x^2+4x }$.
Answer
$$ \left( \color{blue}{-2x^2-5x+7} \right) \cdot \left( \color{orangered}{-2x^2+4x} \right) = 4x^4+2x^3-34x^2+28x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-2x^2} & \color{blue}{-5x} & \color{blue}{7} \\ \hline \color{blue}{-2x^2} & & & \\ \hline \color{blue}{4x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-2x^2} & \color{blue}{-5x} & \color{blue}{7} \\ \hline \color{blue}{-2x^2} & \color{orangered}{4x^4} & \color{orangered}{10x^3} & \color{orangered}{-14x^2} \\ \hline \color{blue}{4x} & \color{orangered}{-8x^3} & \color{orangered}{-20x^2} & \color{orangered}{28x} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^4 + 10x^3-8x^3-14x^2-20x^2 + 28x = \\ 4x^4+2x^3-34x^2+28x $$This page was created using
Polynomial Operations Calculator