To identify which of the given polynomials is a difference of two squares, we need to recall the formula for a difference of squares, which is a² – b² = (a + b)(a – b). A polynomial can be classified as such if it can be expressed in this form.
Let’s examine the given options:
- x² – 14: This does not fit because 14 is not a perfect square.
- x² + 14: This is also not a difference of squares because it is a sum, not a difference.
- x² – 49: Here, 49 is a perfect square (7²). Therefore, this can be rewritten as x² – 7². Using the difference of squares formula, we can express it as (x + 7)(x – 7).
- x² + 49: Similar to the second option, this is a sum, not a difference.
Based on this analysis, the polynomial x² – 49 is the only one that qualifies as a difference of two squares.