-(3a-1%2F7b).jpeg "(9а^2-1/49b^2) (3a-1/7b)")
Factoring the Expression (9a² - 1/49b²) (3a - 1/7b)
This expression can be factored using the difference of squares pattern and then simplified. Let's break down the steps:
1. Recognizing the Difference of Squares
The first part of the expression, (9a² - 1/49b²), fits the pattern of the difference of squares:
a² - b² = (a + b)(a - b)
In this case:
- a = 3a
- b = 1/7b
2. Applying the Pattern
Applying the difference of squares pattern, we get:
(9a² - 1/49b²) = (3a + 1/7b)(3a - 1/7b)
3. Combining with the Remaining Factor
Now we can combine this result with the remaining factor, (3a - 1/7b):
4. Simplifying
Notice that we have (3a - 1/7b) as a factor twice. We can simplify this to:
(3a + 1/7b)(3a - 1/7b)²
Final Factored Form
The fully factored expression is: (3a + 1/7b)(3a - 1/7b)²