Find the Product (x-2y)^2

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

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

$(x - 2 y) (x - 2 y)$

Expand $(x - 2 y) (x - 2 y)$ using the FOIL Method.

Apply the distributive property.

$x (x - 2 y) - 2 y (x - 2 y)$

Apply the distributive property.

$x \cdot x + x (- 2 y) - 2 y (x - 2 y)$

Apply the distributive property.

$x \cdot x + x (- 2 y) - 2 y x - 2 y (- 2 y)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x y - 2 y x + 4 y^{2}$

Subtract $2 y x$ from $- 2 x y$ .

Move $y$ .

$x^{2} - 2 x y - 2 x y + 4 y^{2}$

Subtract $2 x y$ from $- 2 x y$ .

$x^{2} - 4 x y + 4 y^{2}$