Which is a perfect square trinomial?(1 point)

Question

Responses

x2−169x squared minus 169

16x2−3x+716 x squared minus 3 x plus 7

4x2−12x+94 x squared minus 12 x plus 9

25x+1

Answer 1

A perfect square trinomial is an expression of the form \( (a \pm b)^2 \), which expands to \( a^2 \pm 2ab + b^2 \).

Let's analyze the provided options:

1. \(x^2 - 169\): This is a difference of squares, not a trinomial.

2. \(16x^2 - 3x + 7\): This does not fit the pattern of a perfect square trinomial.

3. \(4x^2 - 12x + 9\): We can check if this is a perfect square trinomial:

   • Here, \(a^2 = 4x^2\) (so \(a = 2x\))
   • \(b^2 = 9\) (so \(b = 3\))
   • The middle term, \(2ab = -12x\) suggests \(-2(2x)(3) = -12x\).

   Thus, \(4x^2 - 12x + 9 = (2x - 3)^2\), which confirms that it is a perfect square trinomial.

4. \(25x + 1\): This is a linear expression, not a trinomial.

The correct answer is \(4x^2 - 12x + 9\).