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

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

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

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

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

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

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

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