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

Question

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. \( (2x + 8)(2x - 8) \)