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#1. Factor the given polynomials using difference of squares.

You have 13 cards in this activity.
1 are sorted correctly.
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Binomial:

4x2−36

Binomial:

9−25x2

Binomial:

4x2+36

Binomial:

9x2−25

Binomial:

81−49x2

Binomial:

81x2−49

1 answer

To factor the given polynomials using the difference of squares, we will look for expressions of the form \( a^2 - b^2 \), which can be factored as \( (a - b)(a + b) \).

Here are the factorizations for the given binomials:

  1. Binomial: \( 4x^2 - 36 \)

    • Factorization: \( 2(x - 3)(x + 3) \)

  2. Binomial: \( 9 - 25x^2 \)

    • Factorization: \( (3 - 5x)(3 + 5x) \)

  3. Binomial: \( 4x^2 + 36 \)

    • Factorization: Not a difference of squares (cannot be factored using this method).

  4. Binomial: \( 9x^2 - 25 \)

    • Factorization: \( (3x - 5)(3x + 5) \)

  5. Binomial: \( 81 - 49x^2 \)

    • Factorization: \( (9 - 7x)(9 + 7x) \)

  6. Binomial: \( 81x^2 - 49 \)

    • Factorization: \( (9x - 7)(9x + 7) \)

To summarize:

  • \( 4x^2 - 36 = 2(x - 3)(x + 3) \)
  • \( 9 - 25x^2 = (3 - 5x)(3 + 5x) \)
  • \( 4x^2 + 36 \) cannot be factored using difference of squares.
  • \( 9x^2 - 25 = (3x - 5)(3x + 5) \)
  • \( 81 - 49x^2 = (9 - 7x)(9 + 7x) \)
  • \( 81x^2 - 49 = (9x - 7)(9x + 7) \)

Make sure to highlight only the difference of squares to be correct in your sorting!