Precalculus Examples

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

Simplify the left side $x^{2} + {(y - 9)}^{2}$ .

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Simplify each term.

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

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Remove parentheses.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $y$ by $y$ by adding the exponents.

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Combine $y$ and $y$

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Raise $y$ to the power of $1$ .

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

Raise $y$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} + (y^{1 + 1} + y \cdot - 9 - 9 y - 9 \cdot - 9) = 25$

Add $1$ and $1$ .

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

Move $- 9$ to the left of the expression $y \cdot - 9$ .

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

Multiply $- 9$ by $y$ .

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

Multiply $- 9$ by $- 9$ .

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

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

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

Remove unnecessary parentheses.

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

Move $25$ to the left side of the equation by subtracting it from both sides.

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

Subtract $25$ from $81$ .

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

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