We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{-6x} & \color{blue}{-5} \\ \hline \color{blue}{7x^2} & & & \\ \hline \color{blue}{6x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{-6x} & \color{blue}{-5} \\ \hline \color{blue}{7x^2} & \color{orangered}{42x^4} & \color{orangered}{-42x^3} & \color{orangered}{-35x^2} \\ \hline \color{blue}{6x} & \color{orangered}{36x^3} & \color{orangered}{-36x^2} & \color{orangered}{-30x} \\ \hline \color{blue}{-5} & \color{orangered}{-30x^2} & \color{orangered}{30x} & \color{orangered}{25} \\ \hline \end{darray} $$

Combine like terms:

$$ 42x^4-42x^3 + 36x^3-35x^2-36x^2-30x^2-30x + 30x + 25 = \\ 42x^4-6x^3-101x^2+25 $$

Polynomial Operations Calculator