Simplify (2x-2)^2-(2x-2)

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $2$ by $- 2$ .

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

Multiply $- 2$ by $- 2$ .

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

Subtract $4 x$ from $- 4 x$ .

$4 x^{2} - 8 x + 4 - (2 x - 2)$

Apply the distributive property.

$4 x^{2} - 8 x + 4 - (2 x) - - 2$

Multiply $2$ by $- 1$ .

$4 x^{2} - 8 x + 4 - 2 x - - 2$

Multiply $- 1$ by $- 2$ .

$4 x^{2} - 8 x + 4 - 2 x + 2$

Simplify by adding terms.

Subtract $2 x$ from $- 8 x$ .

$4 x^{2} - 10 x + 4 + 2$

Add $4$ and $2$ .

$4 x^{2} - 10 x + 6$