Precalculus Examples

$x^{2} + {(y - 9)}^{2} = 25$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(y - 9)}^{2}$ as $(y - 9) (y - 9)$ .

$x^{2} + (y - 9) (y - 9) = 25$

Step 1.2

Expand $(y - 9) (y - 9)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x^{2} + y (y - 9) - 9 (y - 9) = 25$

Step 1.2.2

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 9 - 9 (y - 9) = 25$

Step 1.2.3

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 9 - 9 y - 9 \cdot - 9 = 25$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 9 - 9 y - 9 \cdot - 9 = 25$

Step 1.3.1.2

Move $- 9$ to the left of $y$ .

$x^{2} + y^{2} - 9 \cdot y - 9 y - 9 \cdot - 9 = 25$

Step 1.3.1.3

Multiply $- 9$ by $- 9$ .

$x^{2} + y^{2} - 9 y - 9 y + 81 = 25$

Step 1.3.2

Subtract $9 y$ from $- 9 y$ .

$x^{2} + y^{2} - 18 y + 81 = 25$

Step 2

Subtract $25$ from both sides of the equation.

$x^{2} + y^{2} - 18 y + 81 - 25 = 0$

Step 3

Subtract $25$ from $81$ .

$x^{2} + y^{2} - 18 y + 56 = 0$

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