Factors of x³ − x²y − xy² + y³
The factors of \[ x^3-x^2y-xy^2+y^3 \] are
(a) \((x+y)(x^2-xy+y^2)\)
(b) \((x+y)(x^2+xy+y^2)\)
(c) \((x+y)^2(x-y)\)
(d) \((x-y)^2(x+y)\)
Solution
\[ x^3-x^2y-xy^2+y^3 \]
\[ =x^2(x-y)-y^2(x-y) \]
\[ =(x-y)(x^2-y^2) \]
\[ =(x-y)^2(x+y) \]
\[ \boxed{(d)\ (x-y)^2(x+y)} \]