Simplify the algebraic expression (x2) / (x-2)2 and state its domain.

The expression is:

$$\frac{x^2}{(x-2)^2}$$

The denominator is a binomial squared, $(x-2)^2$. Using the formula $(a-b)^2 = a^2 - 2ab + b^2$:

$$(x-2)^2 = x^2 - 2(x)(2) + 2^2$$ $$(x-2)^2 = x^2 - 4x + 4$$

Substitute the expanded denominator back into the expression:

$$\frac{x^2}{x^2 - 4x + 4}$$

For the expression to be defined, the denominator cannot be zero.

$$(x-2)^2 \neq 0$$ $$x-2 \neq 0$$ $$x \neq 2$$

The expression is defined for all real numbers $x$ except $x=2$.