Find the Expanded Form (x-3)^2+(y-1)^2=16

${(x - 3)}^{2} + {(y - 1)}^{2} = 16$

Step 1

Simplify the left side ${(x - 3)}^{2} + {(y - 1)}^{2}$ .

Simplify each term.

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

$(x - 3) (x - 3) + {(y - 1)}^{2} = 16$

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

Apply the distributive property.

$x (x - 3) - 3 (x - 3) + {(y - 1)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) + {(y - 1)}^{2} = 16$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 1)}^{2} = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 1)}^{2} = 16$

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

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + {(y - 1)}^{2} = 16$

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 + {(y - 1)}^{2} = 16$

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

$x^{2} - 6 x + 9 + {(y - 1)}^{2} = 16$

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

$x^{2} - 6 x + 9 + (y - 1) (y - 1) = 16$

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

Apply the distributive property.

$x^{2} - 6 x + 9 + y (y - 1) - 1 (y - 1) = 16$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 1 - 1 (y - 1) = 16$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 16$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 6 x + 9 + y^{2} + y \cdot - 1 - 1 y - 1 \cdot - 1 = 16$

Move $- 1$ to the left of $y$ .

$x^{2} - 6 x + 9 + y^{2} - 1 \cdot y - 1 y - 1 \cdot - 1 = 16$

Rewrite $- 1 y$ as $- y$ .

$x^{2} - 6 x + 9 + y^{2} - y - 1 y - 1 \cdot - 1 = 16$

Rewrite $- 1 y$ as $- y$ .

$x^{2} - 6 x + 9 + y^{2} - y - y - 1 \cdot - 1 = 16$

Multiply $- 1$ by $- 1$ .

$x^{2} - 6 x + 9 + y^{2} - y - y + 1 = 16$

Subtract $y$ from $- y$ .

$x^{2} - 6 x + 9 + y^{2} - 2 y + 1 = 16$

Simplify the expression.

Add $9$ and $1$ .

$x^{2} - 6 x + y^{2} - 2 y + 10 = 16$

Move $- 6 x$ .

$x^{2} + y^{2} - 6 x - 2 y + 10 = 16$

Step 2

Subtract $16$ from both sides of the equation.

$x^{2} + y^{2} - 6 x - 2 y + 10 - 16 = 0$

Step 3

Subtract $16$ from $10$ .

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

Find the Expanded Form (x-3)^2+(y-1)^2=16

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