Factor the polynomial: a^2 - b ^2 + 3 a - 3 b?

(a^2 - b^2) + (3a - 3b)
(a-b)(a+b) + 3(a-b)
(a-b)(a+b+3)

(a - b)(a + b) + 3 (a - b)

(a - b) (a + b + 3)

a^2 - b^2 + 3a - 3b
= (a^2 - b^2) + (3a - 3b)
= (a + b)(a - b) + 3(a - b)
= [a + b][(a - b) + 3]
= [a + b][a - b + 3]

a^2 - b^2 is the difference of squares

a^2 - b^2 + 3a - 3b
= (a+b)(a-b) + 3(a-b)
= (a+b+3)(a-b)

a^2 - b^2 + 3a - 3b
= a^2 + 3a - b^2 - 3b
= a(a + 3) - b(b + 3)

(a-b)(a+b+3)