Find the Expanded Form (x-3)^2+(y-2)^2=100

${(x - 3)}^{2} + {(y - 2)}^{2} = 100$

Step 1

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

Simplify each term.

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

$(x - 3) (x - 3) + {(y - 2)}^{2} = 100$

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

Apply the distributive property.

$x (x - 3) - 3 (x - 3) + {(y - 2)}^{2} = 100$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) + {(y - 2)}^{2} = 100$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 2)}^{2} = 100$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 2)}^{2} = 100$

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

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + {(y - 2)}^{2} = 100$

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 + {(y - 2)}^{2} = 100$

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 6 x + 9 + {(y - 2)}^{2} = 100$

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

$x^{2} - 6 x + 9 + (y - 2) (y - 2) = 100$

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

Apply the distributive property.

$x^{2} - 6 x + 9 + y (y - 2) - 2 (y - 2) = 100$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 2 - 2 (y - 2) = 100$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 2 - 2 y - 2 \cdot - 2 = 100$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 6 x + 9 + y^{2} + y \cdot - 2 - 2 y - 2 \cdot - 2 = 100$

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

$x^{2} - 6 x + 9 + y^{2} - 2 \cdot y - 2 y - 2 \cdot - 2 = 100$

Multiply $- 2$ by $- 2$ .

$x^{2} - 6 x + 9 + y^{2} - 2 y - 2 y + 4 = 100$

Subtract $2 y$ from $- 2 y$ .

$x^{2} - 6 x + 9 + y^{2} - 4 y + 4 = 100$

Simplify the expression.

Add $9$ and $4$ .

$x^{2} - 6 x + y^{2} - 4 y + 13 = 100$

Move $- 6 x$ .

$x^{2} + y^{2} - 6 x - 4 y + 13 = 100$

Step 2

Subtract $100$ from both sides of the equation.

$x^{2} + y^{2} - 6 x - 4 y + 13 - 100 = 0$

Step 3

Subtract $100$ from $13$ .

$x^{2} + y^{2} - 6 x - 4 y - 87 = 0$

Find the Expanded Form (x-3)^2+(y-2)^2=100

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