How do you factor the expression #x^3 - x^2y - y^3 + xy^2#?

1 Answer
Jul 1, 2016

Answer:

#x^3 - x^2y - y^3 + xy^2=(x-y)(x^2+y^2)#

Explanation:

#x^3 - x^2y - y^3 + xy^2 = y^3((x/y)^3-(x/y)^2+(x/y)-1)#

but

#z^3-z^2+z-1 =0# has a root #z = 1#

making

#z^3-z^2+z-1 = (z-1)(b z^2+c z+ d)#

equating the coefficients we find

#{ (d-1 = 0), (c - d + 1= 0),( b - c -1= 0), (1 - b = 0) :}#

solving for #b,c,d#

#(b=1,c=0,d=1)#

so

#z^3-z^2+z-1 = (z-1)(z^2+ 1)#

and finally

#x^3 - x^2y - y^3 + xy^2=(x-y)(x^2+y^2)#