-(3a-1%2F7b).jpeg "(9a^2-1/49b^2) (3a-1/7b)")
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:
- First: (3a)(3a) = 9a^2
- Outer: (3a)(-1/7b) = -3/7ab
- Inner: (1/7b)(3a) = 3/7ab
- Last: (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)