Question
Multiply polynomial $ \, \color{blue}{ 7x^2+2x-7 } \, $ by $ \, \color{orangered}{ 7x+3 }$.
Answer
$$ \left( \color{blue}{7x^2+2x-7} \right) \cdot \left( \color{orangered}{7x+3} \right) = 49x^3+35x^2-43x-21 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^2} & \color{blue}{2x} & \color{blue}{-7} \\ \hline \color{blue}{7x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^2} & \color{blue}{2x} & \color{blue}{-7} \\ \hline \color{blue}{7x} & \color{orangered}{49x^3} & \color{orangered}{14x^2} & \color{orangered}{-49x} \\ \hline \color{blue}{3} & \color{orangered}{21x^2} & \color{orangered}{6x} & \color{orangered}{-21} \\ \hline \end{darray} $$Combine like terms:
$$ 49x^3 + 14x^2 + 21x^2-49x + 6x-21 = \\ 49x^3+35x^2-43x-21 $$This page was created using
Polynomial Operations Calculator