Question

59³- 41³
______ +59×41=
18

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Answer 1

a³ - b³ = (a - b)(a² + ab + b²)
(a + b)² = a² + 2ab + b²

(59³- 41³)/18 + 59*41 = (59 - 41)(59² + 59*41 + 41²)/18 + 59*41 = 18*(59² + 59*41 + 41²)/18 + 59*41 = 59² + 59*41 +41² + 59*41 = 59² + 2*59*41 +41² = (59 + 41)² = 100² = 10000