Find the Expanded Form (x-11)^2+(y+2)^2=16

${(x - 11)}^{2} + {(y + 2)}^{2} = 16$

Step 1

Simplify the left side ${(x - 11)}^{2} + {(y + 2)}^{2}$ .

Simplify each term.

Rewrite ${(x - 11)}^{2}$ as $(x - 11) (x - 11)$ .

$(x - 11) (x - 11) + {(y + 2)}^{2} = 16$

Expand $(x - 11) (x - 11)$ using the FOIL Method.

Apply the distributive property.

$x (x - 11) - 11 (x - 11) + {(y + 2)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 11 (x - 11) + {(y + 2)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 11 x - 11 \cdot - 11 + {(y + 2)}^{2} = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 11 - 11 x - 11 \cdot - 11 + {(y + 2)}^{2} = 16$

Move $- 11$ to the left of $x$ .

$x^{2} - 11 \cdot x - 11 x - 11 \cdot - 11 + {(y + 2)}^{2} = 16$

Multiply $- 11$ by $- 11$ .

$x^{2} - 11 x - 11 x + 121 + {(y + 2)}^{2} = 16$

Subtract $11 x$ from $- 11 x$ .

$x^{2} - 22 x + 121 + {(y + 2)}^{2} = 16$

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

$x^{2} - 22 x + 121 + (y + 2) (y + 2) = 16$

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

Apply the distributive property.

$x^{2} - 22 x + 121 + y (y + 2) + 2 (y + 2) = 16$

Apply the distributive property.

$x^{2} - 22 x + 121 + y \cdot y + y \cdot 2 + 2 (y + 2) = 16$

Apply the distributive property.

$x^{2} - 22 x + 121 + y \cdot y + y \cdot 2 + 2 y + 2 \cdot 2 = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 22 x + 121 + y^{2} + y \cdot 2 + 2 y + 2 \cdot 2 = 16$

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

$x^{2} - 22 x + 121 + y^{2} + 2 \cdot y + 2 y + 2 \cdot 2 = 16$

Multiply $2$ by $2$ .

$x^{2} - 22 x + 121 + y^{2} + 2 y + 2 y + 4 = 16$

Add $2 y$ and $2 y$ .

$x^{2} - 22 x + 121 + y^{2} + 4 y + 4 = 16$

Simplify the expression.

Add $121$ and $4$ .

$x^{2} - 22 x + y^{2} + 4 y + 125 = 16$

Move $- 22 x$ .

$x^{2} + y^{2} - 22 x + 4 y + 125 = 16$

Step 2

Subtract $16$ from both sides of the equation.

$x^{2} + y^{2} - 22 x + 4 y + 125 - 16 = 0$

Step 3

Subtract $16$ from $125$ .

$x^{2} + y^{2} - 22 x + 4 y + 109 = 0$

Find the Expanded Form (x-11)^2+(y+2)^2=16

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