During a full moon, the moon is about 12 times brighter than in the first quarter. Why?

Only due to the phase effect, the illumination created by the Moon on the Earth should have changed only ~ 2 times. However, with an increase in the phase, the surface brightness of the Moon also increases due to the fact that the angle of incidence of solar rays on the surface of the Moon changes, the proportion of light scattered towards the Earth decreases, the shadows cast by the irregularities of the relief on the Moon decrease.