Question
Multiply polynomial $ \, \color{blue}{ x^2-x } \, $ by $ \, \color{orangered}{ x^2-10x+25 }$.
Answer
$$ \left( \color{blue}{x^2-x} \right) \cdot \left( \color{orangered}{x^2-10x+25} \right) = x^4-11x^3+35x^2-25x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-10x} & \color{blue}{25} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-10x} & \color{blue}{25} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-10x^3} & \color{orangered}{25x^2} \\ \hline \color{blue}{-x} & \color{orangered}{-x^3} & \color{orangered}{10x^2} & \color{orangered}{-25x} \\ \hline \end{darray} $$Combine like terms:
$$ x^4-10x^3-x^3 + 25x^2 + 10x^2-25x = \\ x^4-11x^3+35x^2-25x $$This page was created using
Polynomial Operations Calculator