Factorize the algebraic expression (10ab + 4a + 5b + 2).

To factorize the expression 10ab + 4a + 5b + 2, we can use the method of grouping.

Step 1: Group the terms in pairs: (10ab + 4a) + (5b + 2)

Step 2: Factor out the common factors from each pair:

From the first pair (10ab + 4a), we can factor out 2a: 2a(5b + 2)

From the second pair (5b + 2), we can factor out 1: 1(5b + 2)

Step 3: Now, the expression becomes: 2a(5b + 2) + 1(5b + 2)

Step 4: We can factor out the common binomial factor (5b + 2): (5b + 2)(2a + 1)

Thus, the factorized form of the given expression is: (5b + 2)(2a + 1)