1. Given the function $$y = 8(5x^2 - 1)(x^2 - 1)$$, we want to find the second derivative $$y''$$. 2. First, expand the function: $$y = 8((5x^2)(x^2) - 5x^2 - x^2 + 1) = 8(5x^4 -6x^2 + 1)$$ 3. Distribute the 8: $$y = 40x^4 - 48x^2 + 8$$ 4. Find the first derivative $$y'$$ using power rule: $$y' = 160x^3 - 96x$$ 5. Find the second derivative $$y''$$ by differentiating $$y'$$: $$y'' = 480x^2 - 96$$ 6. Therefore, the second derivative is $$y'' = 480x^2 - 96$$.