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 $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

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 $0$ .

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