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Which trinomial is a perfect square trinomial? Responses a²- 4a + 64 a 2 - 4 a + 64 a² - 12a + 36 a 2 - 12 a + 36 a² - 6a + 36 a 2 - 6 a + 36 a²- 8a + 64

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Final answer:

The trinomial a² - 12a + 36 is a perfect square trinomial because it can be expressed as (a - 6)^2, meeting the criteria for a perfect square.

Step-by-step explanation:

To determine which trinomial is a perfect square trinomial, we need to consider the standard form of a perfect square trinomial, which is (a + b)^2 = a^2 + 2ab + b^2. For a trinomial to be a perfect square, the middle term must be twice the product of the square roots of the first and third terms. Among the given options, the trinomial a² - 12a + 36 meets this condition because it can be written as (a - 6)^2 with a middle term of -12a (which is twice the product of a and 6) and constant term 36 (which is 6^2). Thus, this trinomial is a perfect square trinomial.

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