(2√5-4√2)·(2√2+√5) =
(√6-2√3)² =
(2√5 - 4√2)·(2√2 + √5) =2√5 * 2√2 + 2√5 * √5 - 4√2 * 2√2 - 4√2 * √5 = 4√10 + 10 - 16 - 4√10 = -6
(√6-2√3)² = √6² - 2 * √6 * 2√3 + (2√3)² = 6 - 4√18 + 12 = 18 - 4√(9 * 2) = 18 - 12√2
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(2√5 - 4√2)·(2√2 + √5) =2√5 * 2√2 + 2√5 * √5 - 4√2 * 2√2 - 4√2 * √5 = 4√10 + 10 - 16 - 4√10 = -6
(√6-2√3)² = √6² - 2 * √6 * 2√3 + (2√3)² = 6 - 4√18 + 12 = 18 - 4√(9 * 2) = 18 - 12√2