Question
Multiply polynomial $ \, \color{blue}{ x^2-10x+25 } \, $ by $ \, \color{orangered}{ 2x+7 }$.
Answer
$$ \left( \color{blue}{x^2-10x+25} \right) \cdot \left( \color{orangered}{2x+7} \right) = 2x^3-13x^2-20x+175 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-10x} & \color{blue}{25} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{7} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-10x} & \color{blue}{25} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{-20x^2} & \color{orangered}{50x} \\ \hline \color{blue}{7} & \color{orangered}{7x^2} & \color{orangered}{-70x} & \color{orangered}{175} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3-20x^2 + 7x^2 + 50x-70x + 175 = \\ 2x^3-13x^2-20x+175 $$This page was created using
Polynomial Operations Calculator