Factorize : `2sqrt(2)x^3+3sqrt(3)y^3+sqrt(5)(5-3sqrt(6)x y)`

Explanation

Given,
`2sqrt(2)x^3+3sqrt(3)y^3+sqrt5(5−3sqrt(6)xy)`
`=2sqrt(2)x^3+3sqrt(3)y^3+5sqrt5−3sqrt6xxsqrt(5)xy`
`=(sqrt(2)x)^3+(sqrt(3)y)^3+(sqrt5)^3−3×sqrt(2)x×sqrt(3)y×sqrt(5)`
`a^3+b^3+c^3−3abc=(a+b+c)(a^2+b^2+c^2−ab−bc−ca)`
⇒`(sqrt(2)x+sqrt(3)y+sqrt5)(2x^2+3y^2+5−sqrt(6)xy−sqrt(5)y−sqrt(10)x)`