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

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

Step 1

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 4$ by $- 4$ .

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

Subtract $4 x$ from $- 4 x$ .

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

Reorder.

Move $16$ .

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

Move $- 8 x$ .

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

Step 2

Subtract $16$ from both sides of the equation.

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

Step 3

Combine the opposite terms in $x^{2} + y^{2} - 8 x + 16 - 16$ .

Subtract $16$ from $16$ .

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

Add $x^{2} + y^{2} - 8 x$ and $0$ .

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