Which is a perfect square trinomial?

Question

Reference Sheet - Perfect Square Trinomial

(1 point)
Responses

16x2−9
16
𝑥
2
−
9
16 x squared minus 9

16x+3
16
𝑥
+
3
16 x plus 3

16x2+24x+9
16
𝑥
2
+
24
𝑥
+
9
16 x squared plus 24 x plus 9

16x2−4x+3

Answer 1

A perfect square trinomial is a quadratic expression that can be rewritten as the square of a binomial. The general forms of perfect square trinomials are:

1. \( (a + b)^2 = a^2 + 2ab + b^2 \)
2. \( (a - b)^2 = a^2 - 2ab + b^2 \)

Looking at your options, we can analyze the third option:

16x² + 24x + 9

1. \( a^2 = 16x^2 \) (where \( a = 4x \))
2. \( b^2 = 9 \) (where \( b = 3 \))
3. The middle term \( 24x \) should equal \( 2ab = 2(4x)(3) = 24x \).

Since all these conditions are satisfied, 16x² + 24x + 9 is indeed a perfect square trinomial, specifically:

\((4x + 3)^2\).

The other options are not perfect square trinomials.

So, the correct answer is:

16x² + 24x + 9.