Find the Expanded Form (x-5)^2+(y-2)^2=25

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

Step 1

Simplify the left side ${(x - 5)}^{2} + {(y - 2)}^{2}$ .

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 (x - 5) + {(y - 2)}^{2} = 25$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 + {(y - 2)}^{2} = 25$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 + {(y - 2)}^{2} = 25$

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

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5 + {(y - 2)}^{2} = 25$

Multiply $- 5$ by $- 5$ .

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

Subtract $5 x$ from $- 5 x$ .

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

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

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

Expand $(y - 2) (y - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$x^{2} - 10 x + 25 + y \cdot y + y \cdot - 2 - 2 (y - 2) = 25$

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

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

Move $- 2$ to the left of $y$ .

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

Multiply $- 2$ by $- 2$ .

$x^{2} - 10 x + 25 + y^{2} - 2 y - 2 y + 4 = 25$

Subtract $2 y$ from $- 2 y$ .

$x^{2} - 10 x + 25 + y^{2} - 4 y + 4 = 25$

Simplify the expression.

Add $25$ and $4$ .

$x^{2} - 10 x + y^{2} - 4 y + 29 = 25$

Move $- 10 x$ .

$x^{2} + y^{2} - 10 x - 4 y + 29 = 25$

Step 2

Subtract $25$ from both sides of the equation.

$x^{2} + y^{2} - 10 x - 4 y + 29 - 25 = 0$

Step 3

Subtract $25$ from $29$ .

$x^{2} + y^{2} - 10 x - 4 y + 4 = 0$

Find the Expanded Form (x-5)^2+(y-2)^2=25

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