Find the Expanded Form (x-6)^2+(y-4)^2=56

${(x - 6)}^{2} + {(y - 4)}^{2} = 56$

Step 1

Simplify the left side ${(x - 6)}^{2} + {(y - 4)}^{2}$ .

Simplify each term.

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$(x - 6) (x - 6) + {(y - 4)}^{2} = 56$

Expand $(x - 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$x (x - 6) - 6 (x - 6) + {(y - 4)}^{2} = 56$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 (x - 6) + {(y - 4)}^{2} = 56$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 + {(y - 4)}^{2} = 56$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 + {(y - 4)}^{2} = 56$

Move $- 6$ to the left of $x$ .

$x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 + {(y - 4)}^{2} = 56$

Multiply $- 6$ by $- 6$ .

$x^{2} - 6 x - 6 x + 36 + {(y - 4)}^{2} = 56$

Subtract $6 x$ from $- 6 x$ .

$x^{2} - 12 x + 36 + {(y - 4)}^{2} = 56$

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

$x^{2} - 12 x + 36 + (y - 4) (y - 4) = 56$

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

Apply the distributive property.

$x^{2} - 12 x + 36 + y (y - 4) - 4 (y - 4) = 56$

Apply the distributive property.

$x^{2} - 12 x + 36 + y \cdot y + y \cdot - 4 - 4 (y - 4) = 56$

Apply the distributive property.

$x^{2} - 12 x + 36 + y \cdot y + y \cdot - 4 - 4 y - 4 \cdot - 4 = 56$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 12 x + 36 + y^{2} + y \cdot - 4 - 4 y - 4 \cdot - 4 = 56$

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

$x^{2} - 12 x + 36 + y^{2} - 4 \cdot y - 4 y - 4 \cdot - 4 = 56$

Multiply $- 4$ by $- 4$ .

$x^{2} - 12 x + 36 + y^{2} - 4 y - 4 y + 16 = 56$

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

$x^{2} - 12 x + 36 + y^{2} - 8 y + 16 = 56$

Simplify the expression.

Add $36$ and $16$ .

$x^{2} - 12 x + y^{2} - 8 y + 52 = 56$

Move $- 12 x$ .

$x^{2} + y^{2} - 12 x - 8 y + 52 = 56$

Step 2

Subtract $56$ from both sides of the equation.

$x^{2} + y^{2} - 12 x - 8 y + 52 - 56 = 0$

Step 3

Subtract $56$ from $52$ .

$x^{2} + y^{2} - 12 x - 8 y - 4 = 0$

Find the Expanded Form (x-6)^2+(y-4)^2=56

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