问题


There is a single choice question about elementary mathematics. Answer the question by replying A, B, C or D.
Question: Which pair of expressions is equivalent for any variable value greater than zero?
A. 3(x+2) and 3x+2
B. 4d+ 2e and 8d+e
C. f+f+f+g and 3fg
D. b+b+3c and 2b+ 3c
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

D. b+b+3c and 2b+ 3c
D
deepseekr1

The correct answer is D.

**Explanation:**
- **Option A:** Expanding 3(x+2) gives 3x + 6, which differs from 3x + 2. Not equivalent.
- **Option B:** Coefficients for \(d\) (4 vs. 8) and \(e\) (2 vs. 1) are unequal. Substituting values confirms they’re not equivalent.
- **Option C:** Simplifying the left side gives \(3f + g\), while the right side is \(3fg\). These are fundamentally different operations (addition vs. multiplication).
- **Option D:** Combining like terms in \(b + b + 3c\) results in \(2b + 3c\), which matches the second expression exactly. Testing with values confirms equivalence for all \(b, c > 0\).

**Answer:** D
D
gpto1 D D
GPT-4o D. b+b+3c and 2b+ 3c D
llama3.1-70B-Instruct

The correct answer is D
D
llama3.1-405B-Instruct

D. b+b+3c and 2b+ 3c
D
DeepSeek-Coder-V2 D D
Qwen2-72B-Instruct D. b+b+3c and 2b+ 3c D
baichuan4 D D
doubao D

3(x+2) = 3x + 6 ≠ 3x + 2; 4d + 2e ≠ 8d + e; f+f+f+g = 3f + g ≠ 3fg; b+b+3c = 2b + 3c.
D
minimax D. b+b+3c and 2b+ 3c

The expressions b+b+3c and 2b+3c are equivalent because both simplify to the same expression: 2b+3c. The first expression is simply the sum of two b's and one 3c, which is the same as the second expression.
D
kimi D D
wenxinyiyan D

Explanation:
We need to find a pair of expressions that are equivalent for any variable value greater than zero. Let's check each option:

A. 3(x+2) and 3x+2
Expand the first expression: 3(x+2) = 3x + 6. This is not equal to 3x + 2, so this option is incorrect.

B. 4d + 2e and 8d + e
These expressions cannot be simplified to be equivalent, so this option is incorrect.

C. f+f+f+g and 3fg
The first expression simplifies to 3f + g, which is not equal to 3fg. So this option is incorrect.

D. b+b+3c and 2b+3c
The first expression simplifies to 2b + 3c, which is exactly the same as the second expression. So this option is correct.
D
zhipu To determine which pair of expressions is equivalent for any variable value greater than zero, let's simplify and compare each pair:

A. \(3(x + 2)\) and \(3x + 2\)
- Simplifying \(3(x + 2)\) gives \(3x + 6\), which is not equivalent to \(3x + 2\).

B. \(4d + 2e\) and \(8d + e\)
- These expressions cannot be simplified to become equivalent because the coefficients of \(d\) and \(e\) are different.

C. \(f + f + f + g\) and \(3fg\)
- Simplifying \(f + f + f + g\) gives \(3f + g\), which is not equivalent to \(3fg\).

D. \(b + b + 3c\) and \(2b + 3c\)
- Simplifying \(b + b + 3c\) gives \(2b + 3c\), which is equivalent to \(2b + 3c\).

Thus, the correct answer is:

D
D
gpto1 D D
deepseekv3 To determine which pair of expressions is equivalent for any variable value greater than zero, let's analyze each option:

**A.** \( 3(x + 2) \) and \( 3x + 2 \)
*Explanation:*
\( 3(x + 2) = 3x + 6 \), which is not equivalent to \( 3x + 2 \).
**Not equivalent.**

**B.** \( 4d + 2e \) and \( 8d + e \)
*Explanation:*
These expressions are not equivalent because the coefficients of \( d \) and \( e \) are different.
**Not equivalent.**

**C.** \( f + f + f + g \) and \( 3fg \)
*Explanation:*
\( f + f + f + g = 3f + g \), which is not equivalent to \( 3fg \).
**Not equivalent.**

**D.** \( b + b + 3c \) and \( 2b + 3c \)
*Explanation:*
\( b + b + 3c = 2b + 3c \), which is exactly the same as the second expression.
**Equivalent.**

Thus, the correct answer is:

**D.**
D