Find the Expanded Form (x-3)^2+(y-4)^2=4

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

Step 1

Simplify the left side ${(x - 3)}^{2} + {(y - 4)}^{2}$ .

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 3$ by $- 3$ .

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

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

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 4 - 4 (y - 4) = 4$

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

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

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

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

Multiply $- 4$ by $- 4$ .

$x^{2} - 6 x + 9 + y^{2} - 4 y - 4 y + 16 = 4$

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

$x^{2} - 6 x + 9 + y^{2} - 8 y + 16 = 4$

Simplify the expression.

Add $9$ and $16$ .

$x^{2} - 6 x + y^{2} - 8 y + 25 = 4$

Move $- 6 x$ .

$x^{2} + y^{2} - 6 x - 8 y + 25 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$x^{2} + y^{2} - 6 x - 8 y + 25 - 4 = 0$

Step 3

Subtract $4$ from $25$ .

$x^{2} + y^{2} - 6 x - 8 y + 21 = 0$

Find the Expanded Form (x-3)^2+(y-4)^2=4

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