Find the Expanded Form (x-1)^2+(y-5)^2=49

${(x - 1)}^{2} + {(y - 5)}^{2} = 49$

Step 1

Simplify the left side ${(x - 1)}^{2} + {(y - 5)}^{2}$ .

Simplify each term.

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

$(x - 1) (x - 1) + {(y - 5)}^{2} = 49$

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

Apply the distributive property.

$x (x - 1) - 1 (x - 1) + {(y - 5)}^{2} = 49$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 (x - 1) + {(y - 5)}^{2} = 49$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 + {(y - 5)}^{2} = 49$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 + {(y - 5)}^{2} = 49$

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

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 + {(y - 5)}^{2} = 49$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1 + {(y - 5)}^{2} = 49$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1 + {(y - 5)}^{2} = 49$

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1 + {(y - 5)}^{2} = 49$

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1 + {(y - 5)}^{2} = 49$

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

$x^{2} - 2 x + 1 + (y - 5) (y - 5) = 49$

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

Apply the distributive property.

$x^{2} - 2 x + 1 + y (y - 5) - 5 (y - 5) = 49$

Apply the distributive property.

$x^{2} - 2 x + 1 + y \cdot y + y \cdot - 5 - 5 (y - 5) = 49$

Apply the distributive property.

$x^{2} - 2 x + 1 + y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5 = 49$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 2 x + 1 + y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5 = 49$

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

$x^{2} - 2 x + 1 + y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5 = 49$

Multiply $- 5$ by $- 5$ .

$x^{2} - 2 x + 1 + y^{2} - 5 y - 5 y + 25 = 49$

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

$x^{2} - 2 x + 1 + y^{2} - 10 y + 25 = 49$

Simplify the expression.

Add $1$ and $25$ .

$x^{2} - 2 x + y^{2} - 10 y + 26 = 49$

Move $- 2 x$ .

$x^{2} + y^{2} - 2 x - 10 y + 26 = 49$

Step 2

Subtract $49$ from both sides of the equation.

$x^{2} + y^{2} - 2 x - 10 y + 26 - 49 = 0$

Step 3

Subtract $49$ from $26$ .

$x^{2} + y^{2} - 2 x - 10 y - 23 = 0$

Find the Expanded Form (x-1)^2+(y-5)^2=49

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