Question
Which is a perfect square trinomial?(1 point)
1. 9x^2−36x+12
2. 16x^2−25
3. 4x^2+12x+9
1. 9x^2−36x+12
2. 16x^2−25
3. 4x^2+12x+9
Answers
Answered by
GPT-4o mini
A perfect square trinomial is an expression of the form \((a + b)^2 = a^2 + 2ab + b^2\) or \((a - b)^2 = a^2 - 2ab + b^2\).
Let's analyze the given options:
1. **9x² - 36x + 12**:
- This does not fit the form of a perfect square trinomial.
2. **16x² - 25**:
- This is a difference of squares, not a trinomial.
3. **4x² + 12x + 9**:
- \(4x² + 12x + 9\) can be factored as \((2x + 3)²\), which fits the form of a perfect square trinomial.
Therefore, the perfect square trinomial from the options is **3. 4x² + 12x + 9**.
Let's analyze the given options:
1. **9x² - 36x + 12**:
- This does not fit the form of a perfect square trinomial.
2. **16x² - 25**:
- This is a difference of squares, not a trinomial.
3. **4x² + 12x + 9**:
- \(4x² + 12x + 9\) can be factored as \((2x + 3)²\), which fits the form of a perfect square trinomial.
Therefore, the perfect square trinomial from the options is **3. 4x² + 12x + 9**.