Why the Fourier series expansion for $\dfrac{\pi^{2}x-\pi x^{2}}{8}$ $ -\pi \leq x \leq \pi $ cannot be used to find the Fourier series expansion for $\dfrac{\pi^{2}-2 \pi x}{8}$. While the Fourier series expansion $\dfrac{\pi^{2}x-x^{3}}{12}$ can be used to find the Fourier series expansion for $\dfrac{\pi^{2}-3x^{2}}{12}$, $-\pi \leq x\leq \pi$.
I have no idea how to tackle this problem, can someone initiate the starting please!