Simplify (n-1)(2n-2)

$(n - 1) (2 n - 2)$

Step 1

Expand $(n - 1) (2 n - 2)$ using the FOIL Method.

Apply the distributive property.

$n (2 n - 2) - 1 (2 n - 2)$

Apply the distributive property.

$n (2 n) + n \cdot - 2 - 1 (2 n - 2)$

Apply the distributive property.

$n (2 n) + n \cdot - 2 - 1 (2 n) - 1 \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 n \cdot n + n \cdot - 2 - 1 (2 n) - 1 \cdot - 2$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$2 (n \cdot n) + n \cdot - 2 - 1 (2 n) - 1 \cdot - 2$

Multiply $n$ by $n$ .

$2 n^{2} + n \cdot - 2 - 1 (2 n) - 1 \cdot - 2$

Move $- 2$ to the left of $n$ .

$2 n^{2} - 2 \cdot n - 1 (2 n) - 1 \cdot - 2$

Multiply $2$ by $- 1$ .

$2 n^{2} - 2 n - 2 n - 1 \cdot - 2$

Multiply $- 1$ by $- 2$ .

$2 n^{2} - 2 n - 2 n + 2$

Subtract $2 n$ from $- 2 n$ .

$2 n^{2} - 4 n + 2$