Question
Multiply polynomial $ \, \color{blue}{ 7x-5 } \, $ by $ \, \color{orangered}{ 9x^2-4x+2 }$.
Answer
$$ \left( \color{blue}{7x-5} \right) \cdot \left( \color{orangered}{9x^2-4x+2} \right) = 63x^3-73x^2+34x-10 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{-4x} & \color{blue}{2} \\ \hline \color{blue}{7x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{-4x} & \color{blue}{2} \\ \hline \color{blue}{7x} & \color{orangered}{63x^3} & \color{orangered}{-28x^2} & \color{orangered}{14x} \\ \hline \color{blue}{-5} & \color{orangered}{-45x^2} & \color{orangered}{20x} & \color{orangered}{-10} \\ \hline \end{darray} $$Combine like terms:
$$ 63x^3-28x^2-45x^2 + 14x + 20x-10 = \\ 63x^3-73x^2+34x-10 $$This page was created using
Polynomial Operations Calculator