Examples

{(x - 0)}^{2} + {(y - 1)}^{2} = 4

${(x - 0)}^{2} + {(y - 1)}^{2} = 4$

Step 1

Simplify each term.

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Step 1.1

Subtract

0

$0$ from

x

$x$ .

x^{2} + {(y - 1)}^{2} = 4

$x^{2} + {(y - 1)}^{2} = 4$

Step 1.2

Rewrite

{(y - 1)}^{2}

${(y - 1)}^{2}$ as

(y - 1) (y - 1)

$(y - 1) (y - 1)$ .

x^{2} + (y - 1) (y - 1) = 4

$x^{2} + (y - 1) (y - 1) = 4$

Step 1.3

Expand

(y - 1) (y - 1)

$(y - 1) (y - 1)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

x^{2} + y (y - 1) - 1 (y - 1) = 4

$x^{2} + y (y - 1) - 1 (y - 1) = 4$

Step 1.3.2

Apply the distributive property.

x^{2} + y \cdot y + y \cdot - 1 - 1 (y - 1) = 4

$x^{2} + y \cdot y + y \cdot - 1 - 1 (y - 1) = 4$

Step 1.3.3

Apply the distributive property.

x^{2} + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4

$x^{2} + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4$

x^{2} + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4

$x^{2} + y \cdot y + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply

y

$y$ by

y

$y$ .

x^{2} + y^{2} + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4

$x^{2} + y^{2} + y \cdot - 1 - 1 y - 1 \cdot - 1 = 4$

Step 1.4.1.2

Move

- 1

$- 1$ to the left of

y

$y$ .

x^{2} + y^{2} - 1 \cdot y - 1 y - 1 \cdot - 1 = 4

$x^{2} + y^{2} - 1 \cdot y - 1 y - 1 \cdot - 1 = 4$

Step 1.4.1.3

Rewrite

- 1 y

$- 1 y$ as

- y

$- y$ .

x^{2} + y^{2} - y - 1 y - 1 \cdot - 1 = 4

$x^{2} + y^{2} - y - 1 y - 1 \cdot - 1 = 4$

Step 1.4.1.4

Rewrite

- 1 y

$- 1 y$ as

- y

$- y$ .

x^{2} + y^{2} - y - y - 1 \cdot - 1 = 4

$x^{2} + y^{2} - y - y - 1 \cdot - 1 = 4$

Step 1.4.1.5

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

x^{2} + y^{2} - y - y + 1 = 4

$x^{2} + y^{2} - y - y + 1 = 4$

x^{2} + y^{2} - y - y + 1 = 4

$x^{2} + y^{2} - y - y + 1 = 4$

Step 1.4.2

Subtract

y

$y$ from

- y

$- y$ .

x^{2} + y^{2} - 2 y + 1 = 4

$x^{2} + y^{2} - 2 y + 1 = 4$

x^{2} + y^{2} - 2 y + 1 = 4

$x^{2} + y^{2} - 2 y + 1 = 4$

x^{2} + y^{2} - 2 y + 1 = 4

$x^{2} + y^{2} - 2 y + 1 = 4$

Step 2

Subtract

4

$4$ from both sides of the equation.

x^{2} + y^{2} - 2 y + 1 - 4 = 0

$x^{2} + y^{2} - 2 y + 1 - 4 = 0$

Step 3

Subtract

4

$4$ from

1

$1$ .

x^{2} + y^{2} - 2 y - 3 = 0

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

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