Find the Expanded Form (x+6)^2+(y+8)^2=10^2

${(x + 6)}^{2} + {(y + 8)}^{2} = 10^{2}$

Simplify the left side ${(x + 6)}^{2} + {(y + 8)}^{2}$ .

Simplify each term.

Rewrite ${(x + 6)}^{2}$ as $(x + 6) (x + 6)$ .

$(x + 6) (x + 6) + {(y + 8)}^{2} = 10^{2}$

Expand $(x + 6) (x + 6)$ using the FOIL Method.

Apply the distributive property.

$x (x + 6) + 6 (x + 6) + {(y + 8)}^{2} = 10^{2}$

Apply the distributive property.

$x \cdot x + x \cdot 6 + 6 (x + 6) + {(y + 8)}^{2} = 10^{2}$

Apply the distributive property.

$x \cdot x + x \cdot 6 + 6 x + 6 \cdot 6 + {(y + 8)}^{2} = 10^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 6 + 6 x + 6 \cdot 6 + {(y + 8)}^{2} = 10^{2}$

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x + 6 x + 6 \cdot 6 + {(y + 8)}^{2} = 10^{2}$

Multiply $6$ by $6$ .

$x^{2} + 6 x + 6 x + 36 + {(y + 8)}^{2} = 10^{2}$

Add $6 x$ and $6 x$ .

$x^{2} + 12 x + 36 + {(y + 8)}^{2} = 10^{2}$

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

$x^{2} + 12 x + 36 + (y + 8) (y + 8) = 10^{2}$

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

Apply the distributive property.

$x^{2} + 12 x + 36 + y (y + 8) + 8 (y + 8) = 10^{2}$

Apply the distributive property.

$x^{2} + 12 x + 36 + y \cdot y + y \cdot 8 + 8 (y + 8) = 10^{2}$

Apply the distributive property.

$x^{2} + 12 x + 36 + y \cdot y + y \cdot 8 + 8 y + 8 \cdot 8 = 10^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 12 x + 36 + y^{2} + y \cdot 8 + 8 y + 8 \cdot 8 = 10^{2}$

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

$x^{2} + 12 x + 36 + y^{2} + 8 \cdot y + 8 y + 8 \cdot 8 = 10^{2}$

Multiply $8$ by $8$ .

$x^{2} + 12 x + 36 + y^{2} + 8 y + 8 y + 64 = 10^{2}$

Add $8 y$ and $8 y$ .

$x^{2} + 12 x + 36 + y^{2} + 16 y + 64 = 10^{2}$

Simplify the expression.

Add $36$ and $64$ .

$x^{2} + 12 x + y^{2} + 16 y + 100 = 10^{2}$

Move $12 x$ .

$x^{2} + y^{2} + 12 x + 16 y + 100 = 10^{2}$

Raise $10$ to the power of $2$ .

$x^{2} + y^{2} + 12 x + 16 y + 100 = 100$

Subtract $100$ from both sides of the equation.

$x^{2} + y^{2} + 12 x + 16 y + 100 - 100 = 0$

Combine the opposite terms in $x^{2} + y^{2} + 12 x + 16 y + 100 - 100$ .

Subtract $100$ from $100$ .

$x^{2} + y^{2} + 12 x + 16 y + 0 = 0$

Add $x^{2} + y^{2} + 12 x + 16 y$ and $0$ .

$x^{2} + y^{2} + 12 x + 16 y = 0$

Find the Expanded Form (x+6)^2+(y+8)^2=10^2

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