Let's factor the given polynomials using the difference of squares where applicable.
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81x^2 - 49: This can be factored using the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\).
- Here, \(81x^2 = (9x)^2\) and \(49 = 7^2\).
- So, it factors as: \[ (9x - 7)(9x + 7) \]
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9x^2 - 25: This also fits the difference of squares.
- Here, \(9x^2 = (3x)^2\) and \(25 = 5^2\).
- Factoring gives us: \[ (3x - 5)(3x + 5) \]
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81 - 49x^2: Again, this is a difference of squares.
- Here, \(81 = 9^2\) and \(49x^2 = (7x)^2\).
- Thus, it factors as: \[ (9 - 7x)(9 + 7x) \]
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9 - 25x^2: This fits the difference of squares.
- Here, \(9 = 3^2\) and \(25x^2 = (5x)^2\).
- Therefore, it factors as: \[ (3 - 5x)(3 + 5x) \]
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4x^2 - 36: This is a difference of squares as well.
- Here, \(4x^2 = (2x)^2\) and \(36 = 6^2\).
- So, it can be factored as: \[ (2x - 6)(2x + 6) \]
Now, let's summarize the factorizations correctly with attention to the matches:
- 81x^2 - 49 → (9x - 7)(9x + 7)
- 9x^2 - 25 → (3x - 5)(3x + 5)
- 81 - 49x^2 → (9 - 7x)(9 + 7x)
- 9 - 25x^2 → (3 - 5x)(3 + 5x)
- 4x^2 - 36 → (2x - 6)(2x + 6)
Let me know if you need any more help!