Find the Expanded Form (x-2)^2+(y-3)^2=9

${(x - 2)}^{2} + {(y - 3)}^{2} = 9$

Step 1

Simplify the left side ${(x - 2)}^{2} + {(y - 3)}^{2}$ .

Simplify each term.

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

$(x - 2) (x - 2) + {(y - 3)}^{2} = 9$

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

Apply the distributive property.

$x (x - 2) - 2 (x - 2) + {(y - 3)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) + {(y - 3)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + {(y - 3)}^{2} = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 + {(y - 3)}^{2} = 9$

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 + {(y - 3)}^{2} = 9$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 + {(y - 3)}^{2} = 9$

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

$x^{2} - 4 x + 4 + {(y - 3)}^{2} = 9$

Rewrite ${(y - 3)}^{2}$ as $(y - 3) (y - 3)$ .

$x^{2} - 4 x + 4 + (y - 3) (y - 3) = 9$

Expand $(y - 3) (y - 3)$ using the FOIL Method.

Apply the distributive property.

$x^{2} - 4 x + 4 + y (y - 3) - 3 (y - 3) = 9$

Apply the distributive property.

$x^{2} - 4 x + 4 + y \cdot y + y \cdot - 3 - 3 (y - 3) = 9$

Apply the distributive property.

$x^{2} - 4 x + 4 + y \cdot y + y \cdot - 3 - 3 y - 3 \cdot - 3 = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 4 x + 4 + y^{2} + y \cdot - 3 - 3 y - 3 \cdot - 3 = 9$

Move $- 3$ to the left of $y$ .

$x^{2} - 4 x + 4 + y^{2} - 3 \cdot y - 3 y - 3 \cdot - 3 = 9$

Multiply $- 3$ by $- 3$ .

$x^{2} - 4 x + 4 + y^{2} - 3 y - 3 y + 9 = 9$

Subtract $3 y$ from $- 3 y$ .

$x^{2} - 4 x + 4 + y^{2} - 6 y + 9 = 9$

Simplify the expression.

Add $4$ and $9$ .

$x^{2} - 4 x + y^{2} - 6 y + 13 = 9$

Move $- 4 x$ .

$x^{2} + y^{2} - 4 x - 6 y + 13 = 9$

Step 2

Subtract $9$ from both sides of the equation.

$x^{2} + y^{2} - 4 x - 6 y + 13 - 9 = 0$

Step 3

Subtract $9$ from $13$ .

$x^{2} + y^{2} - 4 x - 6 y + 4 = 0$

Find the Expanded Form (x-2)^2+(y-3)^2=9

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