Find the Expanded Form (x-2)^2+(y-4)^2=4

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

Step 1

Simplify the left side ${(x - 2)}^{2} + {(y - 4)}^{2}$ .

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $- 2$ .

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

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

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

Rewrite ${(y - 4)}^{2}$ as $(y - 4) (y - 4)$ .

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

Expand $(y - 4) (y - 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

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

Move $- 4$ to the left of $y$ .

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

Multiply $- 4$ by $- 4$ .

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

Subtract $4 y$ from $- 4 y$ .

$x^{2} - 4 x + 4 + y^{2} - 8 y + 16 = 4$

Simplify the expression.

Add $4$ and $16$ .

$x^{2} - 4 x + y^{2} - 8 y + 20 = 4$

Move $- 4 x$ .

$x^{2} + y^{2} - 4 x - 8 y + 20 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$x^{2} + y^{2} - 4 x - 8 y + 20 - 4 = 0$

Step 3

Subtract $4$ from $20$ .

$x^{2} + y^{2} - 4 x - 8 y + 16 = 0$

Find the Expanded Form (x-2)^2+(y-4)^2=4

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