Question
Multiply polynomial $ \, \color{blue}{ 2x+10 } \, $ by $ \, \color{orangered}{ x^2+4x+4 }$.
Answer
$$ \left( \color{blue}{2x+10} \right) \cdot \left( \color{orangered}{x^2+4x+4} \right) = 2x^3+18x^2+48x+40 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{4} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{10} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{4} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{8x^2} & \color{orangered}{8x} \\ \hline \color{blue}{10} & \color{orangered}{10x^2} & \color{orangered}{40x} & \color{orangered}{40} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 8x^2 + 10x^2 + 8x + 40x + 40 = \\ 2x^3+18x^2+48x+40 $$This page was created using
Polynomial Operations Calculator