Find the Expanded Form (x-0)^2+(y-1)^2=1

${(x - 0)}^{2} + {(y - 1)}^{2} = 1$

Step 1

Simplify each term.

Subtract $0$ from $x$ .

$x^{2} + {(y - 1)}^{2} = 1$

Rewrite ${(y - 1)}^{2}$ as $(y - 1) (y - 1)$ .

$x^{2} + (y - 1) (y - 1) = 1$

Expand $(y - 1) (y - 1)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + y (y - 1) - 1 (y - 1) = 1$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 1 - 1 (y - 1) = 1$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 1$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 1 - 1 y - 1 \cdot - 1 = 1$

Move $- 1$ to the left of $y$ .

$x^{2} + y^{2} - 1 \cdot y - 1 y - 1 \cdot - 1 = 1$

Rewrite $- 1 y$ as $- y$ .

$x^{2} + y^{2} - y - 1 y - 1 \cdot - 1 = 1$

Rewrite $- 1 y$ as $- y$ .

$x^{2} + y^{2} - y - y - 1 \cdot - 1 = 1$

Multiply $- 1$ by $- 1$ .

$x^{2} + y^{2} - y - y + 1 = 1$

Subtract $y$ from $- y$ .

$x^{2} + y^{2} - 2 y + 1 = 1$

Step 2

Subtract $1$ from both sides of the equation.

$x^{2} + y^{2} - 2 y + 1 - 1 = 0$

Step 3

Combine the opposite terms in $x^{2} + y^{2} - 2 y + 1 - 1$ .

Subtract $1$ from $1$ .

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

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

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