In order to factorize the given expression, we find to find two numbers p and q such that:
p + q = 14, pq = 48
Clearly,
8 + 6 = 14, 8 (6) = 48
Therefore, split (14a) as 8a + 6a
Therefore,
a2 + 14a + 48 = a2 + 8a + 6a + 48
= a (a + 8) + 6 (a + 8)
= (a + 6) (a + 8)