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{(√2 + √3) + (2 + √5)} {(-√2 +√3) + (2 - √5)} =
(√2 + √3)(- √2 + √3) + (√2 + √3)(2 - √5) + (2 + √5) (-√2 + √3) + (2 + √5)(2 - √5) =
(3 - 2) + 2√2 - √10 + 2√3 - √15 - 2√2 + 2√3 - √10 + √15 + (4 - 5) =
1 + 2√2 - 2√2 - √10 - √10 + 2√3 + 2√3 - √15 + √15 - 1 =
2√3 - 2√10