Question

गुणनखंड कीजिए :

`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`

Answer 1

`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)]`  ...[सर्वसमिका का प्रयोग करके, 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]`