Simplify (x-y)^2

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

Step 1

Rewrite ${(x - y)}^{2}$ as $(x - y) (x - y)$ .

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 1$ by $- 1$ .

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

Multiply $y^{2}$ by $1$ .

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

Subtract $y x$ from $- x y$ .

Move $y$ .

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

Subtract $x y$ from $- x y$ .

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