## Factoring the Expression: (9a^2 - 1/49b^2)(3a - 1/7b)

This expression involves factoring a difference of squares and then multiplying the resulting binomials. Let's break it down step by step:

### 1. Recognizing the Difference of Squares

Notice that the first part of the expression, **(9a^2 - 1/49b^2)**, is in the form of a difference of squares.

**9a^2**is the square of**3a**.**1/49b^2**is the square of**1/7b**.

Therefore, we can factor it as:

**(9a^2 - 1/49b^2) = (3a + 1/7b)(3a - 1/7b)**

### 2. Multiplying the Binomials

Now, we have the expression:

**(3a + 1/7b)(3a - 1/7b)(3a - 1/7b)**

We can multiply the first two binomials using the FOIL method:

**F**irst: (3a)(3a) = 9a^2**O**uter: (3a)(-1/7b) = -3/7ab**I**nner: (1/7b)(3a) = 3/7ab**L**ast: (1/7b)(-1/7b) = -1/49b^2

Combining the terms, we get:

**(9a^2 - 1/49b^2)(3a - 1/7b) = (9a^2 - 1/49b^2)(3a - 1/7b)**

### 3. Final Result

Therefore, the fully factored expression is:

**(9a^2 - 1/49b^2)(3a - 1/7b) = (3a + 1/7b)(3a - 1/7b)(3a - 1/7b)**