Find the Expanded Form (x+4)^2+(y-2)^2=16

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

Step 1

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $4$ by $4$ .

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

Add $4 x$ and $4 x$ .

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

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

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

Expand $(y - 2) (y - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

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

Move $- 2$ to the left of $y$ .

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

Multiply $- 2$ by $- 2$ .

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

Subtract $2 y$ from $- 2 y$ .

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

Simplify the expression.

Add $16$ and $4$ .

$x^{2} + 8 x + y^{2} - 4 y + 20 = 16$

Move $8 x$ .

$x^{2} + y^{2} + 8 x - 4 y + 20 = 16$

Step 2

Subtract $16$ from both sides of the equation.

$x^{2} + y^{2} + 8 x - 4 y + 20 - 16 = 0$

Step 3

Subtract $16$ from $20$ .

$x^{2} + y^{2} + 8 x - 4 y + 4 = 0$

Find the Expanded Form (x+4)^2+(y-2)^2=16

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