Which is a perfect square trinomial? Reference Sheet - Perfect Square Trinomials(1 point)

Question

Responses

9x2−49
9
𝑥
2
−
49
9 x squared minus 49

9x2+42x+49
9
𝑥
2
+
42
𝑥
+
49
9 x squared plus 42 x plus 49

9x2−42x+12

Answer 1

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. The general form of a perfect square trinomial is either \((a + b)^2\) or \((a - b)^2\), which expands to \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\), respectively.

From your options, let's identify which one is a perfect square trinomial:

1. \(9x^2 - 49\): This is a difference of squares, not a trinomial, and cannot be factored as a perfect square trinomial.

2. \(9x^2 + 42x + 49\): This can be factored as \((3x + 7)^2\). It fits the form \(a^2 + 2ab + b^2\), where \(a = 3x\) and \(b = 7\).

3. \(9x^2 - 42x + 12\): This does not fit the characteristics of a perfect square trinomial.

Therefore, the perfect square trinomial from the given options is \(9x^2 + 42x + 49\).