  Spin-orbit effects appearing in topological insulators (TI) and at Rashba
interfaces are currently revolutionizing how we can manipulate spins and have
led to several newly discovered effects, from spin-charge interconversion and
spin-orbit torques to novel magnetoresistance phenomena. In particular, a
puzzling magnetoresistance has been evidenced, bilinear in electric and
magnetic fields. Here, we report the observation of bilinear magnetoresistance
(BMR) in strained HgTe, a prototypical TI. We show that both the amplitude and
sign of this BMR can be tuned by controlling, with an electric gate, the
relative proportions of the opposite contributions of opposite surfaces. At
magnetic fields of 1 T, the magnetoresistance is of the order of 1 \% and has a
larger figure of merit than previously measured TIs. We propose a theoretical
model giving a quantitative account of our experimental data. This phenomenon,
unique to TI, offers novel opportunities to tune their electrical response for
spintronics.
