In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = 2, pq = -3

Clearly,

p = 3, q = -1

Therefore, split (2a) as (3a – a)

Therefore,

a² + 2a – 3 = a² + 3a – a – 3

= a (a + 3) – 1 (a + 3)

= (a – 1) (a + 3)