Question
Multiply polynomial $ \, \color{blue}{ 2x+2 } \, $ by $ \, \color{orangered}{ x^2+2x+3 }$.
Answer
$$ \left( \color{blue}{2x+2} \right) \cdot \left( \color{orangered}{x^2+2x+3} \right) = 2x^3+6x^2+10x+6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{3} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{3} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{4x^2} & \color{orangered}{6x} \\ \hline \color{blue}{2} & \color{orangered}{2x^2} & \color{orangered}{4x} & \color{orangered}{6} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 4x^2 + 2x^2 + 6x + 4x + 6 = \\ 2x^3+6x^2+10x+6 $$This page was created using
Polynomial Operations Calculator