So firstly, reverse the signs in (6x^2 + 8x - 1) and change the minus sign to a plus sign:
[tex] \begin{alignedat}{2} 4x^2-9x+7\\ +(-6x^2)-8x+1\end{alignedat} [/tex]
Next, combine like terms:
[tex] \begin{alignedat}{3} 4x^2-9x+7\\ +(-6x^2)-8x+1\\-2x^2-17x+8\end{alignedat} [/tex]
The difference is -2x^2 - 17x + 8
