Find the Expanded Form (x-7)^2+(y+8)^2=64

${(x - 7)}^{2} + {(y + 8)}^{2} = 64$

Step 1

Simplify the left side ${(x - 7)}^{2} + {(y + 8)}^{2}$ .

Simplify each term.

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

$(x - 7) (x - 7) + {(y + 8)}^{2} = 64$

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

Apply the distributive property.

$x (x - 7) - 7 (x - 7) + {(y + 8)}^{2} = 64$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 (x - 7) + {(y + 8)}^{2} = 64$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7 + {(y + 8)}^{2} = 64$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7 + {(y + 8)}^{2} = 64$

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

$x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7 + {(y + 8)}^{2} = 64$

Multiply $- 7$ by $- 7$ .

$x^{2} - 7 x - 7 x + 49 + {(y + 8)}^{2} = 64$

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

$x^{2} - 14 x + 49 + {(y + 8)}^{2} = 64$

Rewrite ${(y + 8)}^{2}$ as $(y + 8) (y + 8)$ .

$x^{2} - 14 x + 49 + (y + 8) (y + 8) = 64$

Expand $(y + 8) (y + 8)$ using the FOIL Method.

Apply the distributive property.

$x^{2} - 14 x + 49 + y (y + 8) + 8 (y + 8) = 64$

Apply the distributive property.

$x^{2} - 14 x + 49 + y \cdot y + y \cdot 8 + 8 (y + 8) = 64$

Apply the distributive property.

$x^{2} - 14 x + 49 + y \cdot y + y \cdot 8 + 8 y + 8 \cdot 8 = 64$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 14 x + 49 + y^{2} + y \cdot 8 + 8 y + 8 \cdot 8 = 64$

Move $8$ to the left of $y$ .

$x^{2} - 14 x + 49 + y^{2} + 8 \cdot y + 8 y + 8 \cdot 8 = 64$

Multiply $8$ by $8$ .

$x^{2} - 14 x + 49 + y^{2} + 8 y + 8 y + 64 = 64$

Add $8 y$ and $8 y$ .

$x^{2} - 14 x + 49 + y^{2} + 16 y + 64 = 64$

Simplify the expression.

Add $49$ and $64$ .

$x^{2} - 14 x + y^{2} + 16 y + 113 = 64$

Move $- 14 x$ .

$x^{2} + y^{2} - 14 x + 16 y + 113 = 64$

Step 2

Subtract $64$ from both sides of the equation.

$x^{2} + y^{2} - 14 x + 16 y + 113 - 64 = 0$

Step 3

Subtract $64$ from $113$ .

$x^{2} + y^{2} - 14 x + 16 y + 49 = 0$

Find the Expanded Form (x-7)^2+(y+8)^2=64

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