Simplify (x-y)(y-x)

$(x - y) (y - x)$

Expand $(x - y) (y - x)$ using the FOIL Method.

Apply the distributive property.

$x (y - x) - y (y - x)$

Apply the distributive property.

$x y + x (- x) - y (y - x)$

Apply the distributive property.

$x y + x (- x) - y \cdot y - y (- x)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$x y - x \cdot x - y \cdot y - y (- x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x y - (x \cdot x) - y \cdot y - y (- x)$

Multiply $x$ by $x$ .

$x y - x^{2} - y \cdot y - y (- x)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$x y - x^{2} - (y \cdot y) - y (- x)$

Multiply $y$ by $y$ .

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

Rewrite using the commutative property of multiplication.

$x y - x^{2} - y^{2} - 1 \cdot - 1 y x$

Multiply $- 1$ by $- 1$ .

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

Multiply $y$ by $1$ .

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

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

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

Add $x y$ and $x y$ .

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