Find the Expanded Form x^2+(y+2)^2=4

$x^{2} + {(y + 2)}^{2} = 4$

Step 1

Simplify each term.

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

$x^{2} + (y + 2) (y + 2) = 4$

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

Apply the distributive property.

$x^{2} + y (y + 2) + 2 (y + 2) = 4$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot 2 + 2 (y + 2) = 4$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot 2 + 2 y + 2 \cdot 2 = 4$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot 2 + 2 y + 2 \cdot 2 = 4$

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

$x^{2} + y^{2} + 2 \cdot y + 2 y + 2 \cdot 2 = 4$

Multiply $2$ by $2$ .

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

Add $2 y$ and $2 y$ .

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

Step 2

Subtract $4$ from both sides of the equation.

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

Step 3

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 $0$ .

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