Question

#1. Factor the given polynomials using difference of squares.
You have 13 cards in this activity.
1 are sorted correctly.
A card sort is on the screen. To start dragging a card, Tab to it and press M to mark it. Next, Tab to the card where you want to drop, and press J to join the two cards together. To unjoin the selected card from a group, press U.
Binomial:



4x2−36

Binomial:



9−25x2

Binomial:



4x2+36

Binomial:



9x2−25

Binomial:



81−49x2

Binomial:



81x2−49

Answer 1

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!