Question

Match the difference of squares with its factored form.(1 point)

x^2−49
9x^2−4
4x^2−64

1. (2x+8) (2x-8)
2. (x+7) (x-7)
3. (3x+2) (3x-2)

Answer 1

Let's match each expression to its factored form:

1. **For \( x^2 - 49 \):**
- This is a difference of squares, where \( a^2 - b^2 = (a + b)(a - b) \).
- Here, \( a = x \) and \( b = 7 \) (since \( 49 = 7^2 \)).
- So, \( x^2 - 49 = (x + 7)(x - 7) \).
- This matches option **2**.

2. **For \( 9x^2 - 4 \):**
- This is also a difference of squares where \( a^2 - b^2 = (a + b)(a - b) \).
- Here, \( a = 3x \) and \( b = 2 \) (since \( 4 = 2^2 \)).
- So, \( 9x^2 - 4 = (3x + 2)(3x - 2) \).
- This matches option **3**.

3. **For \( 4x^2 - 64 \):**
- Again, this is a difference of squares.
- Here, \( a = 2x \) and \( b = 8 \) (since \( 64 = 8^2 \)).
- So, \( 4x^2 - 64 = (2x + 8)(2x - 8) \).
- This matches option **1**.

To summarize:

- \( x^2 - 49 \): 2. \( (x + 7)(x - 7) \)
- \( 9x^2 - 4 \): 3. \( (3x + 2)(3x - 2) \)
- \( 4x^2 - 64 \): 1. \( (2x + 8)(2x - 8) \)