Find the Expanded Form (x-0)^2+(y-2)^2=2^2

${(x - 0)}^{2} + {(y - 2)}^{2} = 2^{2}$

Step 1

Simplify each term.

Subtract $0$ from $x$ .

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 2 - 2 y - 2 \cdot - 2 = 2^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 2 - 2 y - 2 \cdot - 2 = 2^{2}$

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

$x^{2} + y^{2} - 2 \cdot y - 2 y - 2 \cdot - 2 = 2^{2}$

Multiply $- 2$ by $- 2$ .

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

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

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

Step 2

Raise $2$ to the power of $2$ .

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

Step 3

Subtract $4$ from both sides of the equation.

$x^{2} + y^{2} - 4 y + 4 - 4 = 0$

Step 4

Combine the opposite terms in $x^{2} + y^{2} - 4 y + 4 - 4$ .

Subtract $4$ from $4$ .

$x^{2} + y^{2} - 4 y + 0 = 0$

Add $x^{2} + y^{2} - 4 y$ and $0$ .

$x^{2} + y^{2} - 4 y = 0$