Select the expression that is equal to: (3k+1)2.

Question

BlackTom AI · Accepted Answer

Multiplying the binomial by 2 uses the distributive property: 2(3k+1) = 2·3k + 2·1.

Step-by-step calculation:
1. Apply the distributive law: 2(3k+1) = 2×3k + 2×1.
2. Multiply coefficients: 2×3k = (2×3)k = 6k.
3. Multiply constant: 2×1 = 2.
4. Combine terms: 6k + 2.

Thus the expression simplifies to 6k + 2.

Interpreting the answer choices: the option written as "32k+2" can be read as 3·2k + 2, i.e. (3×2)k + 2 = 6k + 2. Therefore "32k+2" is algebraically equivalent to 6k + 2 and matches the simplified result.

Why the other choices are incorrect:
- "3k+2" equals 3k + 2, which is not equal to 6k + 2 except in the special case k = 0.
- "3k+3" equals 3k + 3, differing from 6k + 2 for general k (they would be equal only for a particular k value).
- "32k+1" (interpreted as 3·2k + 1 = 6k + 1) differs from 6k + 2 by 1, so it is not equivalent to the product.

Conclusion: Using the distributive property yields 6k + 2, which corresponds to the listed option "32k+2"; therefore the correct choice is 32k+2, matching the provided answer.

Select the expression that is equal to: (3k+1)2.单项选择题

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