How to expand and simplify? 2( √(15) - 3 √(5))^(2) ​

Question

How to expand and simplify?


`2( √(15) - 3 √(5))^(2)`
​

Answer 1

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