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Question
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
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Solution
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
= `(sqrt(2)a)^3 + (2b)^3 + (-3c)^3 - 3(sqrt(2)a)(2b)(-3c)`
= `(sqrt(2)a + 2b - 3c)[(sqrt(2)a)^2 + (2b)^2 + (-3c)^2 - (sqrt(2)a)(2b) - (2b)(-3c) - (-3c)(sqrt(2)a)]` ...[Using identity, a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)]
= `(sqrt(2)a + 2b - 3c)[2a^2 + 4b^2 + 9c^2 - 2sqrt(2)ab + 6bc + 3sqrt(2)ac]`
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