Find the Expanded Form ((x-8)^2)/2+((y+1)^2)/4=64

$\frac{{(x - 8)}^{2}}{2} + \frac{{(y + 1)}^{2}}{4} = 64$

Step 1

Simplify the left side $\frac{{(x - 8)}^{2}}{2} + \frac{{(y + 1)}^{2}}{4}$ .

To write $\frac{{(x - 8)}^{2}}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{{(x - 8)}^{2}}{2} \cdot \frac{2}{2} + \frac{{(y + 1)}^{2}}{4} = 64$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{{(x - 8)}^{2}}{2}$ by $\frac{2}{2}$ .

$\frac{{(x - 8)}^{2} \cdot 2}{2 \cdot 2} + \frac{{(y + 1)}^{2}}{4} = 64$

Multiply $2$ by $2$ .

$\frac{{(x - 8)}^{2} \cdot 2}{4} + \frac{{(y + 1)}^{2}}{4} = 64$

Combine the numerators over the common denominator.

$\frac{{(x - 8)}^{2} \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Simplify the numerator.

Rewrite ${(x - 8)}^{2}$ as $(x - 8) (x - 8)$ .

$\frac{(x - 8) (x - 8) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Expand $(x - 8) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$\frac{(x (x - 8) - 8 (x - 8)) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Apply the distributive property.

$\frac{(x \cdot x + x \cdot - 8 - 8 (x - 8)) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Apply the distributive property.

$\frac{(x \cdot x + x \cdot - 8 - 8 x - 8 \cdot - 8) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{(x^{2} + x \cdot - 8 - 8 x - 8 \cdot - 8) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Move $- 8$ to the left of $x$ .

$\frac{(x^{2} - 8 \cdot x - 8 x - 8 \cdot - 8) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Multiply $- 8$ by $- 8$ .

$\frac{(x^{2} - 8 x - 8 x + 64) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Subtract $8 x$ from $- 8 x$ .

$\frac{(x^{2} - 16 x + 64) \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Apply the distributive property.

$\frac{x^{2} \cdot 2 - 16 x \cdot 2 + 64 \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Simplify.

Move $2$ to the left of $x^{2}$ .

$\frac{2 \cdot x^{2} - 16 x \cdot 2 + 64 \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Multiply $2$ by $- 16$ .

$\frac{2 \cdot x^{2} - 32 x + 64 \cdot 2 + {(y + 1)}^{2}}{4} = 64$

Multiply $64$ by $2$ .

$\frac{2 \cdot x^{2} - 32 x + 128 + {(y + 1)}^{2}}{4} = 64$

Rewrite ${(y + 1)}^{2}$ as $(y + 1) (y + 1)$ .

$\frac{2 x^{2} - 32 x + 128 + (y + 1) (y + 1)}{4} = 64$

Expand $(y + 1) (y + 1)$ using the FOIL Method.

Apply the distributive property.

$\frac{2 x^{2} - 32 x + 128 + y (y + 1) + 1 (y + 1)}{4} = 64$

Apply the distributive property.

$\frac{2 x^{2} - 32 x + 128 + y \cdot y + y \cdot 1 + 1 (y + 1)}{4} = 64$

Apply the distributive property.

$\frac{2 x^{2} - 32 x + 128 + y \cdot y + y \cdot 1 + 1 y + 1 \cdot 1}{4} = 64$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$\frac{2 x^{2} - 32 x + 128 + y^{2} + y \cdot 1 + 1 y + 1 \cdot 1}{4} = 64$

Multiply $y$ by $1$ .

$\frac{2 x^{2} - 32 x + 128 + y^{2} + y + 1 y + 1 \cdot 1}{4} = 64$

Multiply $y$ by $1$ .

$\frac{2 x^{2} - 32 x + 128 + y^{2} + y + y + 1 \cdot 1}{4} = 64$

Multiply $1$ by $1$ .

$\frac{2 x^{2} - 32 x + 128 + y^{2} + y + y + 1}{4} = 64$

Add $y$ and $y$ .

$\frac{2 x^{2} - 32 x + 128 + y^{2} + 2 y + 1}{4} = 64$

Add $128$ and $1$ .

$\frac{2 x^{2} - 32 x + y^{2} + 2 y + 129}{4} = 64$

Step 2

Multiply both sides by $4$ .

$\frac{2 x^{2} - 32 x + y^{2} + 2 y + 129}{4} \cdot 4 = 64 \cdot 4$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{2 x^{2} - 32 x + y^{2} + 2 y + 129}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2 x^{2} - 32 x + y^{2} + 2 y + 129}{4} \cdot 4 = 64 \cdot 4$

Rewrite the expression.

$2 x^{2} - 32 x + y^{2} + 2 y + 129 = 64 \cdot 4$

Move $- 32 x$ .

$2 x^{2} + y^{2} - 32 x + 2 y + 129 = 64 \cdot 4$

Simplify the right side.

Multiply $64$ by $4$ .

$2 x^{2} + y^{2} - 32 x + 2 y + 129 = 256$

Step 4

Set the equation equal to zero.

Subtract $256$ from both sides of the equation.

$2 x^{2} + y^{2} - 32 x + 2 y + 129 - 256 = 0$

Subtract $256$ from $129$ .

$2 x^{2} + y^{2} - 32 x + 2 y - 127 = 0$

Find the Expanded Form ((x-8)^2)/2+((y+1)^2)/4=64

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