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

${(x - 1)}^{2} + y^{2} = 1$

Step 1

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

Simplify each term.

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

$(x - 1) (x - 1) + y^{2} = 1$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) - 1 (x - 1) + y^{2} = 1$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1 + y^{2} = 1$

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1 + y^{2} = 1$

Reorder.

Move $1$ .

$x^{2} - 2 x + y^{2} + 1 = 1$

Move $- 2 x$ .

$x^{2} + y^{2} - 2 x + 1 = 1$

Step 2

Subtract $1$ from both sides of the equation.

$x^{2} + y^{2} - 2 x + 1 - 1 = 0$

Step 3

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

Subtract $1$ from $1$ .

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

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

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