Question

Which one of the following answer choices is a perfect square trinomial?

A) 25n^2 - 60n + 36
B) n^2 - n - 12
C) 16n^2 - 1
D) 4n^4 - 16n + 10

Answer 1

The perfect square trinomial among the given choices is 25n² - 60n + 36.

Step-by-step explanation:

To determine which of the given trinomials is a perfect square, we need to look for the pattern of the trinomial being in the form of (a + b)². In this form, both 'a' and 'b' are perfect squares.

Let's analyze each answer choice:

1. A) 25n² - 60n + 36 = (5n - 6)², since 5n² - 6n + 6n - 6² = 5n² - 12n + 36
2. B) n² - n - 12 = not a perfect square trinomial
3. C) 16n² - 1 = not a perfect square trinomial
4. D) 4n⁴ - 16n + 10 = not a perfect square trinomial

Therefore, the correct answer is A) 25n² - 60n + 36, as it is a perfect square trinomial.