Find the Expanded Form (x-1/6)^2+y^2=1/36

${(x - \frac{1}{6})}^{2} + y^{2} = \frac{1}{36}$

Simplify the left side ${(x - \frac{1}{6})}^{2} + y^{2}$ .

Simplify each term.

Rewrite ${(x - \frac{1}{6})}^{2}$ as $(x - \frac{1}{6}) (x - \frac{1}{6})$ .

$(x - \frac{1}{6}) (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Expand $(x - \frac{1}{6}) (x - \frac{1}{6})$ using the FOIL Method.

Apply the distributive property.

$x (x - \frac{1}{6}) - \frac{1}{6} \cdot (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Apply the distributive property.

$x \cdot x + x (- \frac{1}{6}) - \frac{1}{6} \cdot (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Apply the distributive property.

$x \cdot x + x (- \frac{1}{6}) - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- \frac{1}{6}) - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Combine $x$ and $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Combine $x$ and $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Multiply $- \frac{1}{6} (- \frac{1}{6})$ .

Multiply $- 1$ by $- 1$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + 1 (\frac{1}{6}) \cdot \frac{1}{6} + y^{2} = \frac{1}{36}$

Multiply $\frac{1}{6}$ by $1$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{6} \cdot \frac{1}{6} + y^{2} = \frac{1}{36}$

Multiply $\frac{1}{6}$ by $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{6 \cdot 6} + y^{2} = \frac{1}{36}$

Multiply $6$ by $6$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Subtract $\frac{x}{6}$ from $- \frac{x}{6}$ .

$x^{2} - 2 \frac{x}{6} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$x^{2} + 2 (- 1) (\frac{x}{6}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Factor $2$ out of $6$ .

$x^{2} + 2 \cdot (- 1 \frac{x}{2 \cdot 3}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Cancel the common factor.

$x^{2} + 2 \cdot (- 1 \frac{x}{2 \cdot 3}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Rewrite the expression.

$x^{2} - 1 \frac{x}{3} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Rewrite $- 1 \frac{x}{3}$ as $- \frac{x}{3}$ .

$x^{2} - \frac{x}{3} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Reorder.

Move $\frac{1}{36}$ .

$x^{2} - \frac{x}{3} + y^{2} + \frac{1}{36} = \frac{1}{36}$

Move $- \frac{x}{3}$ .

$x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} = \frac{1}{36}$

Subtract $\frac{1}{36}$ from both sides of the equation.

$x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} - \frac{1}{36} = 0$

Combine the opposite terms in $x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} - \frac{1}{36}$ .

Combine the numerators over the common denominator.

$x^{2} + y^{2} - \frac{x}{3} + \frac{1 - 1}{36} = 0$

Subtract $1$ from $1$ .

$x^{2} + y^{2} - \frac{x}{3} + \frac{0}{36} = 0$

Divide $0$ by $36$ .

$x^{2} + y^{2} - \frac{x}{3} + 0 = 0$

Add $x^{2} + y^{2} - \frac{x}{3}$ and $0$ .

$x^{2} + y^{2} - \frac{x}{3} = 0$

Find the Expanded Form (x-1/6)^2+y^2=1/36

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