Question
Factorise: $2\sqrt{2}\text{a}^3 + 8\text{b}^3 - 27\text{c}^3 + 18\sqrt{2}\text{abc}.$
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Answer
We have, $2\sqrt{2}\text{a}^3 + 8\text{b}^3 - 27\text{c}^3 + 18\sqrt{2}\text{abc}.$ $=\big\{(\sqrt{2}\text{a})^3 + (2\text{b})^3 + (-3\text{c})^3 - 3(\sqrt{2}\text{a})(2\text{b})(-3\text{c})\big\}$ $=\big\{\sqrt{2}\text{a} + 2\text{b} -3\text{c}\big\}\big\{(\sqrt{2}\text{a})^2+(2\text{b})^2+(-3\text{c})^2-(\sqrt{2}\text{a})(2\text{b})-(2\text{b})(-3\text{c})(\sqrt{2}\text{a})\big\}$ $=(\sqrt{2}\text{a} + 2\text{b} -3\text{c})(2\text{a}^2+4\text{b}^2+9\text{c}^2-2\sqrt{2}\text{ab}+6\text{bc}+3\sqrt{2}\text{ca})$
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