Question
Multiply polynomial $ \, \color{blue}{ 2x-7 } \, $ by $ \, \color{orangered}{ 2x^2+2x-1 }$.
Answer
$$ \left( \color{blue}{2x-7} \right) \cdot \left( \color{orangered}{2x^2+2x-1} \right) = 4x^3-10x^2-16x+7 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{2x} & \color{orangered}{4x^3} & \color{orangered}{4x^2} & \color{orangered}{-2x} \\ \hline \color{blue}{-7} & \color{orangered}{-14x^2} & \color{orangered}{-14x} & \color{orangered}{7} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^3 + 4x^2-14x^2-2x-14x + 7 = \\ 4x^3-10x^2-16x+7 $$This page was created using
Polynomial Operations Calculator