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Question
`2sqrt2a^3 + 16sqrt2b^3 + c^3 - 12abc`
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Solution
`= (sqrt2a)^3 + (2sqrt2b)^3 + c^3 - 3 xx sqrt2a xx 2sqrt2b xx c`
`= (sqrt2a _ 2sqrt2b + c)((sqrt2a)^2 + (2sqrt2b)^2 + c^2 - (sqrt2a)(2sqrt2b) - (2sqrt2b)c - (sqrt2a)c)`
`= (sqrt2a + 2sqrtb + c)(2a^2 + 8b^2 + c^2 - 4ab - 2sqrt2bc - sqrt2ac)`
`2sqrt2a^3 + 16sqrt2b^3 + c^3 - 12abc = (sqrt2a + 2sqrt2b + c)(2a^2 + 8b^2 + c^2 - 4ab - 2sqrt2bc - sqrt2ac)`
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