Find the Expanded Form (x+4)^2+(y-4)^2=25

${(x + 4)}^{2} + {(y - 4)}^{2} = 25$

Step 1

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

Simplify each term.

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$(x + 4) (x + 4) + {(y - 4)}^{2} = 25$

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$x (x + 4) + 4 (x + 4) + {(y - 4)}^{2} = 25$

Apply the distributive property.

$x \cdot x + x \cdot 4 + 4 (x + 4) + {(y - 4)}^{2} = 25$

Apply the distributive property.

$x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4 + {(y - 4)}^{2} = 25$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 + 4 x + 4 \cdot 4 + {(y - 4)}^{2} = 25$

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x + 4 x + 4 \cdot 4 + {(y - 4)}^{2} = 25$

Multiply $4$ by $4$ .

$x^{2} + 4 x + 4 x + 16 + {(y - 4)}^{2} = 25$

Add $4 x$ and $4 x$ .

$x^{2} + 8 x + 16 + {(y - 4)}^{2} = 25$

Rewrite ${(y - 4)}^{2}$ as $(y - 4) (y - 4)$ .

$x^{2} + 8 x + 16 + (y - 4) (y - 4) = 25$

Expand $(y - 4) (y - 4)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 8 x + 16 + y (y - 4) - 4 (y - 4) = 25$

Apply the distributive property.

$x^{2} + 8 x + 16 + y \cdot y + y \cdot - 4 - 4 (y - 4) = 25$

Apply the distributive property.

$x^{2} + 8 x + 16 + y \cdot y + y \cdot - 4 - 4 y - 4 \cdot - 4 = 25$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 8 x + 16 + y^{2} + y \cdot - 4 - 4 y - 4 \cdot - 4 = 25$

Move $- 4$ to the left of $y$ .

$x^{2} + 8 x + 16 + y^{2} - 4 \cdot y - 4 y - 4 \cdot - 4 = 25$

Multiply $- 4$ by $- 4$ .

$x^{2} + 8 x + 16 + y^{2} - 4 y - 4 y + 16 = 25$

Subtract $4 y$ from $- 4 y$ .

$x^{2} + 8 x + 16 + y^{2} - 8 y + 16 = 25$

Simplify the expression.

Add $16$ and $16$ .

$x^{2} + 8 x + y^{2} - 8 y + 32 = 25$

Move $8 x$ .

$x^{2} + y^{2} + 8 x - 8 y + 32 = 25$

Step 2

Subtract $25$ from both sides of the equation.

$x^{2} + y^{2} + 8 x - 8 y + 32 - 25 = 0$

Step 3

Subtract $25$ from $32$ .

$x^{2} + y^{2} + 8 x - 8 y + 7 = 0$

Find the Expanded Form (x+4)^2+(y-4)^2=25

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