Final answer:
The perfect square trinomial from the given options is C) 4x² - 20xy + 25y², which follows the pattern of a perfect square trinomial a² + 2ab + b².
Step-by-step explanation:
The question asks which of the following is a perfect square trinomial. A perfect square trinomial is of the form (a² + 2ab + b²). It is derived from squaring a binomial expression (a + b)². Let's evaluate each option:
- A) 4x² - 14xy + 25y - Incorrect since it's not a trinomial.
- B) 4x² + 14xy - 25y² - Incorrect as it does not follow the pattern a² + 2ab + b².
- C) 4x² - 20xy + 25y² - This matches the form of a perfect square trinomial. The square of 2x is 4x², and the square of 5y is 25y². The middle term is twice the product of 2x and 5y, which is -20xy. Therefore, it's the correct answer.
- D) 4x² + 20xy - 25y² - Incorrect as the signs do not follow the pattern.
Therefore, the answer is C) 4x² - 20xy + 25y².