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

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

Step 1

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 6$ by $- 6$ .

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

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

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

Reorder.

Move $36$ .

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

Move $- 12 x$ .

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

Step 2

Subtract $36$ from both sides of the equation.

$x^{2} + y^{2} - 12 x + 36 - 36 = 0$

Step 3

Combine the opposite terms in $x^{2} + y^{2} - 12 x + 36 - 36$ .

Subtract $36$ from $36$ .

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

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

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