How does the A350 variable camber system decrease drag? Just curious how the A350 reduces drag/fuel burn by extending the flaps ever so slightly during cruise. Everything I've read about extending flaps says that extending them pushes the centre of pressure rearwards. This causes a pitching down moment, which means you need to increase the AoA, but this affects drag and fuel burn negatively (a pitch up command increases the down force from the tailplane which has the result of increasing the effective weight of the plane, which requires an even higher AoA to compensate, which also increases the induced drag).

Here's how it works as per the (A350 Flight Deck and Systems Briefing for Pilots)


  Differential Flap Setting and Variable Camber
  
  The Differential Flap Setting and Variable Camber enable to optimize the loads and drag on the wings.
  Small flaps deflections (4° maximum) either symmetrically or asymmetrically, enable to automatically:
  
  
  Optimize the wing camber to reduce wing loads and drag
  Perform an optimized Lateral Trim function.
Henning Strüber, one of the Airbus engineers behind this system, has written a paper on it.

In cruise:


  This can be applied in early cruise phases to shift the center of lift more inboard and by that reducing the wing root bending moment, which can be transferred into a structural weight saving.


A plane that can be built lighter will have lower drag [for the same payload].

For a heavy and/or a hot and high takeoff:


  In high-lift configuration a more outboard loaded lift distribution can be achieved to reduce induced drag during take-off.


For how that works, see here. The answer there by @PeterKämpf confirms that outboard loading requires a heavy wing relative to the whole mass (scaling laws work for an insect, but not for an albatross or an airplane). So those two regimes may appear to be contradictory: if the cruise system allows a lighter wing, then how can that lighter wing achieve more outboard lift for a heavy takeoff.

Accounting for the gust loads in cruise is the key here, which are smaller for takeoffs. (Thanks to @PeterKämpf for this insight; see comment posted below.)