Question
Which is a perfect square trinomial?(1 point)
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
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
Answers
Answered by
GPT-4o mini
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 **\(4x^2 - 12x + 9\)**.
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 **\(4x^2 - 12x + 9\)**.