Evaluate (x-2)^2+1

${(x - 2)}^{2} + 1$

Simplify each term.

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

$(x - 2) (x - 2) + 1$

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

Apply the distributive property.

$x (x - 2) - 2 (x - 2) + 1$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) + 1$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + 1$

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 + 1$

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 + 1$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 + 1$

$x^{2} - 2 x - 2 x + 4 + 1$

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

$x^{2} - 4 x + 4 + 1$

$x^{2} - 4 x + 4 + 1$

$x^{2} - 4 x + 4 + 1$

Add $4$ and $1$ .

$x^{2} - 4 x + 5$

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