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 $y$ .

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

Multiply $y$ by $1$ .

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

Multiply $y$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $y$ and $y$ .

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

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 $0$ .

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