By the distributive property,
2 (√15 - 3√5)² = 2 (√15 - 3√5) (√15 - 3√5)
… = 2 ((√15)² + 2 (√15) (-3√5) + (-3√5)²)
In other words, we use the identity
(a + b)² = a² + 2ab + b²
with a = √15 and b = -3√5.
Then
2 (√15 - 3√5)² = 2 (15 - 6√(15•5) + 9•5)
… = 2 (15 - 6√(3•5²) + 9•5)
… = 2 (15 - 30√3 + 45)
… = 2 (60 - 30√3)
… = 120 - 60√3
