Question

Factorise:2x 3 -xy 2 -y 3

Answer 1

Let    P(x)  =  2 x³ - x y² - y³
We see that if x = y, then P(x=y) = 0.   Then by Remainder and factor theorem, (x - y) is a factor.

let   P(x) = (x - y) [ 2 x² - a x y + y² ]
               =  2 x³ - a x² y + x y² - 2 x² y + a x y² - y³
               = 2 x³ - (a+2) x² y + (a+1) x y² - y³

By comparing coefficients:  a = -2

P(x) = ( x - y) [2 x² + 2 x y + y² ]

Answer 2

Here is the answer

We can expand the middle term and also solve