Find the Expanded Form (x-2)^2+(y+1)^2=16

${(x - 2)}^{2} + {(y + 1)}^{2} = 16$

Simplify the left side ${(x - 2)}^{2} + {(y + 1)}^{2}$ .

Simplify each term.

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

$(x - 2) (x - 2) + {(y + 1)}^{2} = 16$

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

Apply the distributive property.

$x (x - 2) - 2 (x - 2) + {(y + 1)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) + {(y + 1)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + {(y + 1)}^{2} = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 + {(y + 1)}^{2} = 16$

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 + {(y + 1)}^{2} = 16$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 + {(y + 1)}^{2} = 16$

Subtract $2 x$ from $- 2 x$ .

$x^{2} - 4 x + 4 + {(y + 1)}^{2} = 16$

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

$x^{2} - 4 x + 4 + (y + 1) (y + 1) = 16$

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

Apply the distributive property.

$x^{2} - 4 x + 4 + y (y + 1) + 1 (y + 1) = 16$

Apply the distributive property.

$x^{2} - 4 x + 4 + y \cdot y + y \cdot 1 + 1 (y + 1) = 16$

Apply the distributive property.

$x^{2} - 4 x + 4 + y \cdot y + y \cdot 1 + 1 y + 1 \cdot 1 = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 4 x + 4 + y^{2} + y \cdot 1 + 1 y + 1 \cdot 1 = 16$

Multiply $y$ by $1$ .

$x^{2} - 4 x + 4 + y^{2} + y + 1 y + 1 \cdot 1 = 16$

Multiply $y$ by $1$ .

$x^{2} - 4 x + 4 + y^{2} + y + y + 1 \cdot 1 = 16$

Multiply $1$ by $1$ .

$x^{2} - 4 x + 4 + y^{2} + y + y + 1 = 16$

Add $y$ and $y$ .

$x^{2} - 4 x + 4 + y^{2} + 2 y + 1 = 16$

Simplify the expression.

Add $4$ and $1$ .

$x^{2} - 4 x + y^{2} + 2 y + 5 = 16$

Move $- 4 x$ .

$x^{2} + y^{2} - 4 x + 2 y + 5 = 16$

Subtract $16$ from both sides of the equation.

$x^{2} + y^{2} - 4 x + 2 y + 5 - 16 = 0$

Subtract $16$ from $5$ .

$x^{2} + y^{2} - 4 x + 2 y - 11 = 0$

Find the Expanded Form (x-2)^2+(y+1)^2=16

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