Find the Expanded Form x^2+(y-5)^2=30

$x^{2} + {(y - 5)}^{2} = 30$

Step 1

Simplify each term.

Rewrite ${(y - 5)}^{2}$ as $(y - 5) (y - 5)$ .

$x^{2} + (y - 5) (y - 5) = 30$

Expand $(y - 5) (y - 5)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + y (y - 5) - 5 (y - 5) = 30$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 5 - 5 (y - 5) = 30$

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5 = 30$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5 = 30$

Move $- 5$ to the left of $y$ .

$x^{2} + y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5 = 30$

Multiply $- 5$ by $- 5$ .

$x^{2} + y^{2} - 5 y - 5 y + 25 = 30$

Subtract $5 y$ from $- 5 y$ .

$x^{2} + y^{2} - 10 y + 25 = 30$

Step 2

Subtract $30$ from both sides of the equation.

$x^{2} + y^{2} - 10 y + 25 - 30 = 0$

Step 3

Subtract $30$ from $25$ .

$x^{2} + y^{2} - 10 y - 5 = 0$