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Question
`3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc`
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Solution
`= (sqrt3a)^3 + (-b)^3 + (-sqrt5c)^3 - 3 xx (sqrt3a)(-b)(-sqrt5c)`
`= (sqrt3a + (-b) + (-sqrt5c))((sqrt3a)^2 + (-b)^2 + (-sqrt5c)^2 - sqrt3a(-b)- (-b)(-sqrt5c) - (-sqrt5c)sqrt3a)`
`= (sqrt3a - b - sqrt5c)(3a^2 +b^2 + 5c^2 + sqrt3ab - sqrt5bc + sqrt15ac)`
`∴ 3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc = (sqrt3a - b - sqrt5c)(3a^2 + b^2 + 5c^2 + sqrt3ab - sqrt5bc + sqrt15ac)`
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