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

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

Step 1

Factor $- 1$ out of $a$ .

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

Step 2

Factor $- 1$ out of $- b$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

Reorder terms.

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

Step 8

Cancel the common factor.

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

Step 9

Rewrite the expression.

$1$