Question
Multiply polynomial $ \, \color{blue}{ 4x^2-2x-2 } \, $ by $ \, \color{orangered}{ 4x+6 }$.
Answer
$$ \left( \color{blue}{4x^2-2x-2} \right) \cdot \left( \color{orangered}{4x+6} \right) = 16x^3+16x^2-20x-12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-2x} & \color{blue}{-2} \\ \hline \color{blue}{4x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-2x} & \color{blue}{-2} \\ \hline \color{blue}{4x} & \color{orangered}{16x^3} & \color{orangered}{-8x^2} & \color{orangered}{-8x} \\ \hline \color{blue}{6} & \color{orangered}{24x^2} & \color{orangered}{-12x} & \color{orangered}{-12} \\ \hline \end{darray} $$Combine like terms:
$$ 16x^3-8x^2 + 24x^2-8x-12x-12 = \\ 16x^3+16x^2-20x-12 $$This page was created using
Polynomial Operations Calculator