$$ \frac{x^3-343}{x+7} \cdot \frac{x^2+14x+49}{x^2+7x+49} = \frac{(x-7)(x^2+7x+49)}{x+7} \cdot \frac{(x+7)^2}{x^2+7x+49} = (x-7)(x+7) = x^2 - 49 $$
Ответ: $$x^2-49$$