Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Subtract $0$ from $x$ .

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

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 $y$ by $y$ .

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

Step 1.4.1.2

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

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

Step 1.4.1.3

Rewrite $- 1 y$ as $- y$ .

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

Step 1.4.1.4

Rewrite $- 1 y$ as $- y$ .

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

Step 1.4.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.4.2

Subtract $y$ from $- y$ .

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

Step 2

Subtract $4$ from both sides of the equation.

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

Step 3

Subtract $4$ from $1$ .

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

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