Factorise : 2√2 x^3 + 3√3 y^3 + √5(5 - 3√6 xy)

Question

Factorise : \(2\sqrt2\,x^3+3\sqrt3\,y^3+\sqrt5(5-3\sqrt6\,xy)\)

Answer 1

\(2\sqrt2\,x^3+3\sqrt3\,y^3+\sqrt5(5-3\sqrt6\,xy)\)

= \(2\sqrt2\,x^3+3\sqrt3\,y^3+5\sqrt5-3\sqrt6\times\sqrt5xy\)

= \((\sqrt2x +\sqrt3y+\sqrt5)(2x^2+3y^2+5^2-\sqrt6xy-\sqrt15y-\sqrt10x).\)

[(∴ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)]