Simplify (x-2)^2+4(x-2)+8

${(x - 2)}^{2} + 4 (x - 2) + 8$

Simplify each term.

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

$(x - 2) (x - 2) + 4 (x - 2) + 8$

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

Apply the distributive property.

$x (x - 2) - 2 (x - 2) + 4 (x - 2) + 8$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) + 4 (x - 2) + 8$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + 4 (x - 2) + 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 + 4 (x - 2) + 8$

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 + 4 (x - 2) + 8$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 + 4 (x - 2) + 8$

Subtract $2 x$ from $- 2 x$ .

$x^{2} - 4 x + 4 + 4 (x - 2) + 8$

Apply the distributive property.

$x^{2} - 4 x + 4 + 4 x + 4 \cdot - 2 + 8$

Multiply $4$ by $- 2$ .

$x^{2} - 4 x + 4 + 4 x - 8 + 8$

Combine the opposite terms in $x^{2} - 4 x + 4 + 4 x - 8 + 8$ .

Add $- 4 x$ and $4 x$ .

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

Add $x^{2}$ and $0$ .

$x^{2} + 4 - 8 + 8$

Add $- 8$ and $8$ .

$x^{2} + 4 + 0$

Add $x^{2} + 4$ and $0$ .

$x^{2} + 4$