Find the Expanded Form (x-7)^2+(y+5)^2=7

${(x - 7)}^{2} + {(y + 5)}^{2} = 7$

Step 1

Simplify the left side ${(x - 7)}^{2} + {(y + 5)}^{2}$ .

Simplify each term.

Rewrite ${(x - 7)}^{2}$ as $(x - 7) (x - 7)$ .

$(x - 7) (x - 7) + {(y + 5)}^{2} = 7$

Expand $(x - 7) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) - 7 (x - 7) + {(y + 5)}^{2} = 7$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 (x - 7) + {(y + 5)}^{2} = 7$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7 + {(y + 5)}^{2} = 7$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7 + {(y + 5)}^{2} = 7$

Move $- 7$ to the left of $x$ .

$x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7 + {(y + 5)}^{2} = 7$

Multiply $- 7$ by $- 7$ .

$x^{2} - 7 x - 7 x + 49 + {(y + 5)}^{2} = 7$

Subtract $7 x$ from $- 7 x$ .

$x^{2} - 14 x + 49 + {(y + 5)}^{2} = 7$

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

$x^{2} - 14 x + 49 + (y + 5) (y + 5) = 7$

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

Apply the distributive property.

$x^{2} - 14 x + 49 + y (y + 5) + 5 (y + 5) = 7$

Apply the distributive property.

$x^{2} - 14 x + 49 + y \cdot y + y \cdot 5 + 5 (y + 5) = 7$

Apply the distributive property.

$x^{2} - 14 x + 49 + y \cdot y + y \cdot 5 + 5 y + 5 \cdot 5 = 7$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 14 x + 49 + y^{2} + y \cdot 5 + 5 y + 5 \cdot 5 = 7$

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

$x^{2} - 14 x + 49 + y^{2} + 5 \cdot y + 5 y + 5 \cdot 5 = 7$

Multiply $5$ by $5$ .

$x^{2} - 14 x + 49 + y^{2} + 5 y + 5 y + 25 = 7$

Add $5 y$ and $5 y$ .

$x^{2} - 14 x + 49 + y^{2} + 10 y + 25 = 7$

Simplify the expression.

Add $49$ and $25$ .

$x^{2} - 14 x + y^{2} + 10 y + 74 = 7$

Move $- 14 x$ .

$x^{2} + y^{2} - 14 x + 10 y + 74 = 7$

Step 2

Subtract $7$ from both sides of the equation.

$x^{2} + y^{2} - 14 x + 10 y + 74 - 7 = 0$

Step 3

Subtract $7$ from $74$ .

$x^{2} + y^{2} - 14 x + 10 y + 67 = 0$

Find the Expanded Form (x-7)^2+(y+5)^2=7

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