Hello All, wishing all memebers a great start to the New-Year! (Happy)

I'm not sure if my working is entirely ok below... Tried using latex..no idea why it didnt work..?

Factorise: [tex] 50x^2-10xy-20y^2 [\math]

10(5x^2-xy+2y^2)

10[(5x^2 - 2y^2) - xy]

10[( \sqrt5x + \sqrt2y)^2 -xy )]

10[( \sqrt5x + \sqrt2y) ( \sqrt5x + \sqrt2y) - 7.32xy ] * completing the square