Factor the given polynomials using difference of squares. To attach cards drag it on top of each other until you see them connect, to detach drag the bottom card away.

81x^2 - 49
9x^2 - 25
(9x - 7) (9x + 7)
81 - 49x^2
9-25x^2
(3x + 5) (3x - 5)
(3 + 5x) (3 - 5x)
(9 + 7x) (9 - 7x)
4x^2 + 36
4x^2 - 36
(2x + 6) (2x - 6)

1 answer

Let's factor the given polynomials using the difference of squares where applicable.

  1. 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: \[ (9x - 7)(9x + 7) \]
  2. 9x^2 - 25: This also fits the difference of squares.

    • Here, \(9x^2 = (3x)^2\) and \(25 = 5^2\).
    • Factoring gives us: \[ (3x - 5)(3x + 5) \]
  3. 81 - 49x^2: Again, this is a difference of squares.

    • Here, \(81 = 9^2\) and \(49x^2 = (7x)^2\).
    • Thus, it factors as: \[ (9 - 7x)(9 + 7x) \]
  4. 9 - 25x^2: This fits the difference of squares.

    • Here, \(9 = 3^2\) and \(25x^2 = (5x)^2\).
    • Therefore, it factors as: \[ (3 - 5x)(3 + 5x) \]
  5. 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!