Simplify v((x-2)^2)

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $- 2$ .

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

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

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

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

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

Rewrite using the commutative property of multiplication.

$v x^{2} - 4 v x + v \cdot 4$

Move $4$ to the left of $v$ .

$v x^{2} - 4 v x + 4 \cdot v$

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

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