Factor by Grouping x^3y^2-x^2y^3-xy^2+y^3

$x^{3} y^{2} - x^{2} y^{3} - x y^{2} + y^{3}$

Factor out the GCF of $y^{2}$ from $x^{3} y^{2} - x^{2} y^{3} - x y^{2} + y^{3}$ .

Factor out the GCF of $y^{2}$ from each term in the polynomial.

Factor out the GCF of $y^{2}$ from the expression $x^{3} y^{2}$ .

$y^{2} (x^{3}) - x^{2} y^{3} - x y^{2} + y^{3}$

Factor out the GCF of $y^{2}$ from the expression $- x^{2} y^{3}$ .

$y^{2} (x^{3}) + y^{2} (- x^{2} y) - x y^{2} + y^{3}$

Factor out the GCF of $y^{2}$ from the expression $- x y^{2}$ .

$y^{2} (x^{3}) + y^{2} (- x^{2} y) + y^{2} (- x) + y^{3}$

Factor out the GCF of $y^{2}$ from the expression $y^{3}$ .

$y^{2} (x^{3}) + y^{2} (- x^{2} y) + y^{2} (- x) + y^{2} (y)$

Since all the terms share a common factor of $y^{2}$ , it can be factored out of each term.

$y^{2} (x^{3} - x^{2} y - x + y)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$y^{2} ((x^{3} - x^{2} y) - x + y)$

Factor out the greatest common factor (GCF) from each group.

$y^{2} (x^{2} (x - 1 y) - (x - y))$

Factor the polynomial by factoring out the greatest common factor, $x - 1 y$ .

$y^{2} ((x - 1 y) (x^{2} - 1))$

Rewrite $- 1 y$ as $- y$ .

$y^{2} ((x - y) (x^{2} - 1))$

Rewrite $1$ as $1^{2}$ .

$y^{2} ((x - y) (x^{2} - 1^{2}))$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$y^{2} ((x - y) ((x + 1) (x - 1)))$

Remove unnecessary parentheses.

$y^{2} ((x - y) (x + 1) (x - 1))$