Simplify v((x-10)^2)

$v ({(x - 10)}^{2})$

Step 1

Rewrite ${(x - 10)}^{2}$ as $(x - 10) (x - 10)$ .

$v ((x - 10) (x - 10))$

Step 2

Expand $(x - 10) (x - 10)$ using the FOIL Method.

Apply the distributive property.

$v (x (x - 10) - 10 (x - 10))$

Apply the distributive property.

$v (x \cdot x + x \cdot - 10 - 10 (x - 10))$

Apply the distributive property.

$v (x \cdot x + x \cdot - 10 - 10 x - 10 \cdot - 10)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$v (x^{2} + x \cdot - 10 - 10 x - 10 \cdot - 10)$

Move $- 10$ to the left of $x$ .

$v (x^{2} - 10 \cdot x - 10 x - 10 \cdot - 10)$

Multiply $- 10$ by $- 10$ .

$v (x^{2} - 10 x - 10 x + 100)$

Subtract $10 x$ from $- 10 x$ .

$v (x^{2} - 20 x + 100)$

Step 4

Apply the distributive property.

$v x^{2} + v (- 20 x) + v \cdot 100$

Step 5

Simplify.

Rewrite using the commutative property of multiplication.

$v x^{2} - 20 v x + v \cdot 100$

Move $100$ to the left of $v$ .

$v x^{2} - 20 v x + 100 \cdot v$

$v x^{2} - 20 v x + 100 v$