Final answer:
Option B) 16y²–x² represents a difference of squares as it can be factored into (4y² - x²), which is equivalent to (4y - x)(4y + x).
Step-by-step explanation:
The question asks which of the given options shows a difference of squares. A difference of squares is a binomial of the form a² - b² which can be factored into (a - b)(a + b). Among the options given, B) 16y²–x² represents a difference of squares because it can be rewritten as (4y)² - (1x)², which can then be factored to (4y - x)(4y + x).
The other options do not represent a difference of squares because:
- A) 10y²– 4x² cannot be factored as a difference of squares since 10 is not a perfect square.
- C) 8x²– 48x + 25 and D) 64x²– 48x + 9 are both trinomials and do not fit the form of a difference of squares.