The problem asks us to factor the linear expression $75a - 35ab$. We need to find the correct factorization from the given options.

1. Problem Description

The problem asks us to factor the linear expression $75a - 35ab$. We need to find the correct factorization from the given options.

2. Solution Steps

First, we find the greatest common factor (GCF) of the two terms $75a$ and $35ab$.

The factors of 75 are 1, 3, 5, 15, 25,

7

5. The factors of 35 are 1, 5, 7,

3

5. The common factors of 75 and 35 are 1 and

5. The greatest common factor is

5. Also, both terms have the variable 'a', so 'a' is also part of the GCF.

Therefore, the GCF of $75a$ and $35ab$ is $5a$.

Now, we factor out $5a$ from the expression $75a - 35ab$:

$75a - 35ab = 5a(15) - 5a(7b) = 5a(15 - 7b)$.

Comparing this with the given options:

$5a(7b - 15)$ - Incorrect

$7a(11 - 5b)$ - Incorrect

$5(15a - 7ab)$ - Incorrect

$5a(15 - 7b)$ - Correct

3. Final Answer

$5a(15 - 7b)$