Simplify ((b-2)^2)/((2-b)^2)

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

Factor $- 1$ out of $b$ .

$\frac{{(- 1 (- b) - 2)}^{2}}{{(2 - b)}^{2}}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{{(- 1 (- b) - 1 (2))}^{2}}{{(2 - b)}^{2}}$

Factor $- 1$ out of $- 1 (- b) - 1 (2)$ .

$\frac{{(- 1 (- b + 2))}^{2}}{{(2 - b)}^{2}}$

Apply the product rule to $- 1 (- b + 2)$ .

$\frac{{(- 1)}^{2} {(- b + 2)}^{2}}{{(2 - b)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\frac{1 {(- b + 2)}^{2}}{{(2 - b)}^{2}}$

Multiply ${(- b + 2)}^{2}$ by $1$ .

$\frac{{(- b + 2)}^{2}}{{(2 - b)}^{2}}$

Reorder terms.

$\frac{{(- b + 2)}^{2}}{{(- b + 2)}^{2}}$

Cancel the common factor.

$\frac{{(- b + 2)}^{2}}{{(- b + 2)}^{2}}$

Rewrite the expression.

$1$