Question
Multiply polynomial $ \, \color{blue}{ x+5 } \, $ by $ \, \color{orangered}{ x^2+5x+25 }$.
Answer
$$ \left( \color{blue}{x+5} \right) \cdot \left( \color{orangered}{x^2+5x+25} \right) = x^3+10x^2+50x+125 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{25} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{25} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{5x^2} & \color{orangered}{25x} \\ \hline \color{blue}{5} & \color{orangered}{5x^2} & \color{orangered}{25x} & \color{orangered}{125} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + 5x^2 + 5x^2 + 25x + 25x + 125 = \\ x^3+10x^2+50x+125 $$This page was created using
Polynomial Operations Calculator