To determine if \( 3xy + 6x \) is the same as \( -3x(y-2) \), we need to simplify and compare both expressions.

First, simplify \( -3x(y-2) \):

\[
-3x(y-2) = -3x \cdot y - (-3x \cdot 2)
\]
\[
-3x(y-2) = -3xy + 6x
\]

Now, compare the simplified form with the original expression:

\[
3xy + 6x \quad \text{and} \quad -3xy + 6x
\]

Clearly, \( 3xy + 6x \) is not the same as \( -3xy + 6x \). They differ in the sign of the \( 3xy \) term.

Thus, \( 3xy + 6x \) is not the same as \( -3x(y-2) \).

Would you like more details or have any questions about this?

Here are some related questions to consider:

1. How do you distribute a negative sign across terms in parentheses?
2. What is the distributive property in algebra?
3. How can you factor out a common term in an expression?
4. What are some common mistakes to avoid when distributing terms?
5. Can you provide another example of simplifying an expression using distribution?
6. How does changing the sign of a term affect an equation?
7. What are some strategies for comparing algebraic expressions?
8. Can you simplify the expression \( 5x(y + 4) - 5x \)?

**Tip:** Always carefully distribute the sign and terms when simplifying expressions to avoid mistakes.

Explore whether the expressions 3xy + 6x and -3x(y-2) are equivalent through step-by-step simplification. This problem involves algebraic manipulation, distribution of terms, and understanding the difference between expressions. Suitable for Grades 7-9.

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