Each problem has one error. What mistake was made? there is not mistake in this solution They should not have distributed the \( x^{3} \) to the \( 6 y^{2} \) It should be +15 \( x^{4} \) When distributing to the \( 5 x \) they forgot to distribute the \( y \)

Let's analyze the statements provided to identify the errors in the solution. 1. **"there is not mistake in this solution"**: This statement claims that there is no mistake, which contradicts the other statements. Therefore, this statement is incorrect. 2. **"They should not have distributed the \( x^{3} \) to the \( 6 y^{2} \)"**: This suggests that distributing \( x^{3} \) to \( 6y^{2} \) was a mistake. However, without context, we cannot determine if this distribution was indeed incorrect. 3. **"It should be +15 \( x^{4} \)"**: This statement implies that the result of a calculation should yield \( +15 x^{4} \). Without knowing the original expression, we cannot confirm if this is correct or not. 4. **"When distributing to the \( 5 x \) they forgot to distribute the \( y \)"**: This indicates that while distributing, the variable \( y \) was overlooked. This could be a valid mistake if \( y \) was indeed part of the expression being distributed. ### Conclusion: The first statement is incorrect as it claims there is no mistake, while the other statements point out potential errors. The most clear mistake seems to be in the last statement, where it suggests that \( y \) was not distributed properly. To summarize, the main error is in the claim that there is no mistake, as the other statements indicate that there are indeed mistakes in the distribution process.