Question
Multiply polynomial $ \, \color{blue}{ x^2+4 } \, $ by $ \, \color{orangered}{ x^2+2x+1 }$.
Answer
$$ \left( \color{blue}{x^2+4} \right) \cdot \left( \color{orangered}{x^2+2x+1} \right) = x^4+2x^3+5x^2+8x+4 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{1} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{1} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{2x^3} & \color{orangered}{x^2} \\ \hline \color{blue}{4} & \color{orangered}{4x^2} & \color{orangered}{8x} & \color{orangered}{4} \\ \hline \end{darray} $$Combine like terms:
$$ x^4 + 2x^3 + 4x^2 + x^2 + 8x + 4 = \\ x^4+2x^3+5x^2+8x+4 $$This page was created using
Polynomial Operations Calculator