27.03.2023 - 17:21

Is x^2 + 4x + 4 a perfect square trinomial?

Is x^2 + 4x + 4 a perfect square trinomial?

Answers (1)
  • donman
    April 1, 2023 в 12:56

    Yes, the trinomial x^2 + 4x + 4 is a perfect square trinomial.

    A perfect square trinomial is a trinomial that can be factored into the square of a binomial. In other words, it is the product of two identical binomials.

    To check if x^2 + 4x + 4 is a perfect square trinomial, we can try to factor it using the following formula:

    (a + b)^2 = a^2 + 2ab + b^2

    In this case, a = x and b = 2, so we have:

    (x + 2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4

    As we can see, x^2 + 4x + 4 is equal to (x + 2)^2, which is the square of the binomial (x + 2). Therefore, x^2 + 4x + 4 is a perfect square trinomial.

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