| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | C. 9(2-x)(2+x) | C |
| deepseekr1 | The expression \(36 - 9x^2\) can be factored using the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\). First, rewrite the expression as \(6^2 - (3x)^2\), which factors into \((6 - 3x)(6 + 3x)\) (Option A). However, factoring out the greatest common factor (GCF) first simplifies the process further. The GCF of 36 and \(9x^2\) is 9, so: \[ 36 - 9x^2 = 9(4 - x^2). \] Next, \(4 - x^2\) is another difference of squares (\(2^2 - x^2\)), leading to: \[ 9(4 - x^2) = 9(2 - x)(2 + x), \] which matches **Option C**. While Options A and B are algebraically equivalent to each other and correct, they do not factor out the GCF. Option C provides the most complete factorization by including the GCF. Thus, the best answer is: **C. 9(2-x)(2+x)**. **Answer: C** |
C |
| gpto1 | C | C |
| GPT-4o | A. (6-3x)(6+3x) | C |
| llama3.1-70B-Instruct | A |
C |
| llama3.1-405B-Instruct | A. (6-3x)(6+3x) |
C |
| DeepSeek-Coder-V2 | C. 9(2-x)(2+x) | C |
| Qwen2-72B-Instruct | C. 9(2-x)(2+x) | C |
| baichuan4 | C | C |
| doubao | C. 9(2-x)(2+x) $36-9x^2=9(4-x^2)=9(2-x)(2+x)$. |
C |
| minimax | The expression $36-9x^2$ is a difference of squares, which can be factored as $a^2 - b^2 = (a - b)(a + b)$. Here, $a^2 = 36$ and $b^2 = 9x^2$, so $a = 6$ and $b = 3x$. Applying the difference of squares formula, we get: $36 - 9x^2 = (6)^2 - (3x)^2 = (6 - 3x)(6 + 3x)$. Therefore, the correct answer is: A. $(6-3x)(6+3x)$ |
C |
| kimi | To factor the expression \(36 - 9x^2\), we can first recognize it as a difference of squares. The difference of squares formula is \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a^2\) is \(36\) and \(b^2\) is \(9x^2\), which means \(a = 6\) and \(b = 3x\). So, we can rewrite the expression as: \[36 - 9x^2 = 6^2 - (3x)^2\] Applying the difference of squares formula: \[6^2 - (3x)^2 = (6 - 3x)(6 + 3x)\] Therefore, the correct answer is: A. \((6-3x)(6+3x)\) |
C |
| wenxinyiyan | C | C |
| zhipu | To factor \(36 - 9x^2\), we can recognize that it is a difference of squares. The general form for a difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). Here, \(36\) is \(6^2\) and \(9x^2\) is \((3x)^2\). So, we can rewrite the expression as: \[ 36 - 9x^2 = 6^2 - (3x)^2 \] Applying the difference of squares formula: \[ 6^2 - (3x)^2 = (6 - 3x)(6 + 3x) \] This matches option A: \[ (6 - 3x)(6 + 3x) \] So, the correct answer is: A. (6-3x)(6+3x) |
C |
| gpto1 | C | C |
| deepseekv3 | To factor the expression \( 36 - 9x^2 \), follow these steps: 1. **Factor out the Greatest Common Factor (GCF):** The GCF of \( 36 \) and \( 9x^2 \) is \( 9 \). So, we factor out \( 9 \): \[ 36 - 9x^2 = 9(4 - x^2) \] 2. **Factor the Remaining Expression:** The expression \( 4 - x^2 \) is a difference of squares, which can be factored as: \[ 4 - x^2 = (2 - x)(2 + x) \] 3. **Combine the Factors:** Putting it all together: \[ 36 - 9x^2 = 9(2 - x)(2 + x) \] Now, let's compare this with the given options: A. \( (6 - 3x)(6 + 3x) \) B. \( (-3x + 6)(3x + 6) \) C. \( 9(2 - x)(2 + x) \) D. \( 3(2 + x)^2 \) The correct factorization is **C**. \boxed{C} |
C |