Find the Product (2x-y)^2

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

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

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

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Simplify each term.

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Rewrite using the commutative property of multiplication.

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

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

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Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot - 1 x y - y (2 x) - y (- y)$

Multiply $2$ by $- 1$ .

$4 x^{2} - 2 x y - y (2 x) - y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 2 x y - 1 \cdot 2 y x - y (- y)$

Multiply $- 1$ by $2$ .

$4 x^{2} - 2 x y - 2 y x - y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 2 x y - 2 y x - 1 \cdot - 1 y \cdot y$

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

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Move $y$ .

$4 x^{2} - 2 x y - 2 y x - 1 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} - 2 x y - 2 y x - 1 \cdot - 1 y^{2}$

Multiply $- 1$ by $- 1$ .

$4 x^{2} - 2 x y - 2 y x + 1 y^{2}$

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

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

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

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Move $y$ .

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

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

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