Factor (a+b)(a-b)-(a-b)(a-b)

$(a + b) (a - b) - (a - b) (a - b)$

Step 1

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

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

$(a - b) (a + b) - (a - b) (a - b)$

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

$(a - b) (a + b) + (a - b) (- 1 (a - b))$

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

$(a - b) (a + b - 1 (a - b))$

Step 2

Apply the distributive property.

$(a - b) (a + b - 1 a - 1 (- b))$

Step 3

Rewrite $- 1 a$ as $- a$ .

$(a - b) (a + b - a - 1 (- b))$

Step 4

Multiply $- 1 (- b)$ .

Multiply $- 1$ by $- 1$ .

$(a - b) (a + b - a + 1 b)$

Multiply $b$ by $1$ .

$(a - b) (a + b - a + b)$

Step 5

Subtract $a$ from $a$ .

$(a - b) (b + 0 + b)$

Step 6

Add $b$ and $0$ .

$(a - b) (b + b)$

Step 7

Factor.

Add $b$ and $b$ .

$(a - b) (2 b)$

Remove unnecessary parentheses.

$(a - b) \cdot 2 b$