Question Number 42719 by jbm last updated on 01/Sep/18
Commented by Joel578 last updated on 02/Sep/18
$$\mathrm{Sophie}\:\mathrm{Germain} \\ $$$${p}^{\mathrm{4}} \:+\:\mathrm{4}{q}^{\mathrm{4}} \:=\:\left({p}^{\mathrm{2}} \:+\:\mathrm{2}{pq}\:+\:\mathrm{2}{q}^{\mathrm{2}} \right)\left({p}^{\mathrm{2}} \:−\:\mathrm{2}{pq}\:+\:\mathrm{2}{q}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\left({p}\:+\:{q}\right)^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \right)\left(\left({p}\:−\:{q}\right)^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \right) \\ $$