Find the Expanded Form (x-6)^2+(y-8)^2=10^2

${(x - 6)}^{2} + {(y - 8)}^{2} = 10^{2}$

Step 1

Simplify the left side ${(x - 6)}^{2} + {(y - 8)}^{2}$ .

Simplify each term.

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

$(x - 6) (x - 6) + {(y - 8)}^{2} = 10^{2}$

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

Apply the distributive property.

$x (x - 6) - 6 (x - 6) + {(y - 8)}^{2} = 10^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 (x - 6) + {(y - 8)}^{2} = 10^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 + {(y - 8)}^{2} = 10^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 + {(y - 8)}^{2} = 10^{2}$

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

$x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 + {(y - 8)}^{2} = 10^{2}$

Multiply $- 6$ by $- 6$ .

$x^{2} - 6 x - 6 x + 36 + {(y - 8)}^{2} = 10^{2}$

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

$x^{2} - 12 x + 36 + {(y - 8)}^{2} = 10^{2}$

Rewrite ${(y - 8)}^{2}$ as $(y - 8) (y - 8)$ .

$x^{2} - 12 x + 36 + (y - 8) (y - 8) = 10^{2}$

Expand $(y - 8) (y - 8)$ using the FOIL Method.

Apply the distributive property.

$x^{2} - 12 x + 36 + y (y - 8) - 8 (y - 8) = 10^{2}$

Apply the distributive property.

$x^{2} - 12 x + 36 + y \cdot y + y \cdot - 8 - 8 (y - 8) = 10^{2}$

Apply the distributive property.

$x^{2} - 12 x + 36 + y \cdot y + y \cdot - 8 - 8 y - 8 \cdot - 8 = 10^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 12 x + 36 + y^{2} + y \cdot - 8 - 8 y - 8 \cdot - 8 = 10^{2}$

Move $- 8$ to the left of $y$ .

$x^{2} - 12 x + 36 + y^{2} - 8 \cdot y - 8 y - 8 \cdot - 8 = 10^{2}$

Multiply $- 8$ by $- 8$ .

$x^{2} - 12 x + 36 + y^{2} - 8 y - 8 y + 64 = 10^{2}$

Subtract $8 y$ from $- 8 y$ .

$x^{2} - 12 x + 36 + y^{2} - 16 y + 64 = 10^{2}$

Simplify the expression.

Add $36$ and $64$ .

$x^{2} - 12 x + y^{2} - 16 y + 100 = 10^{2}$

Move $- 12 x$ .

$x^{2} + y^{2} - 12 x - 16 y + 100 = 10^{2}$

Step 2

Raise $10$ to the power of $2$ .

$x^{2} + y^{2} - 12 x - 16 y + 100 = 100$

Step 3

Subtract $100$ from both sides of the equation.

$x^{2} + y^{2} - 12 x - 16 y + 100 - 100 = 0$

Step 4

Combine the opposite terms in $x^{2} + y^{2} - 12 x - 16 y + 100 - 100$ .

Subtract $100$ from $100$ .

$x^{2} + y^{2} - 12 x - 16 y + 0 = 0$

Add $x^{2} + y^{2} - 12 x - 16 y$ and $0$ .

$x^{2} + y^{2} - 12 x - 16 y = 0$

Find the Expanded Form (x-6)^2+(y-8)^2=10^2

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