Which is a perfect square trinomial? Reference Sheet - Perfect Square Trinomial (1 point) Responses x2−100 x squared minus 100 4x2−16x+16 4 x squared minus 16 x plus 16 x2−3x−9 x squared minus 3 x minus 9 49x+16 49 x plus 16

Answer 1

A perfect square trinomial is an expression that can be written in the form \((a + b)^2\) or \((a - b)^2\), which expands to \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\) respectively.

From the options you've provided, the expression \(4x^2 - 16x + 16\) can be analyzed:

1. Identify \(a^2\), \(2ab\), and \(b^2\):
   • \(a^2 = 4x^2\) → \(a = 2x\)
   • \(b^2 = 16\) → \(b = 4\)
   • Check if \(2ab = -16x\):
     • \(2(2x)(4) = 16x\) (which means it should actually be \(-16x\))

Thus, \(4x^2 - 16x + 16 = (2x - 4)^2\), confirming that it is indeed a perfect square trinomial.

The other options do not represent perfect square trinomials based on their structures.

Therefore, the perfect square trinomial from your list is 4x² − 16x + 16.