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The image presents a mathematical discussion in French with two characters expressing different viewpoints.

The first character says:  
"**Le produit d'un nombre par son opposé est toujours négatif.**"  
This translates to: "The product of a number by its opposite is always negative."

The second character responds:  
"**En es-tu vraiment sûre ?**"  
Which means: "Are you really sure about that?"

The question posed at the bottom is:  
"**Que peut-on penser de cette affirmation ? Expliquer.**"  
This translates to: "What can we think of this statement? Explain."

### Explanation:
The statement that "the product of a number by its opposite is always negative" is almost always true **except when the number is zero**. When multiplying a non-zero number by its opposite, the product will indeed be negative. For example:

- \( 5 \times (-5) = -25 \)
- \( -7 \times 7 = -49 \)

However, **if the number is zero**, the product of zero and its opposite (which is still zero) will be **zero**, not negative:

- \( 0 \times (-0) = 0 \)

Thus, the statement is not entirely accurate. It should be corrected to: "The product of a non-zero number by its opposite is always negative."

Would you like to explore more on this concept or need further clarification?

Here are some related questions for further exploration:
1. What is the opposite of a number, and how is it defined?
2. Why is the product of zero and any number always zero?
3. What happens when you multiply two negative numbers together?
4. Can you give examples of real-life situations where opposite numbers are used?
5. How does the concept of opposites apply to other mathematical operations like addition or division?

**Tip**: Always check special cases like zero when evaluating general mathematical statements.

Le produit d'un nombre par son opposé est toujours négatif. En es-tu vraiment sûre ? Que peut-on penser de cette affirmation ? Expliquer.

Explore the validity of the statement 'The product of a number and its opposite is always negative.' Learn why this is true except when the number is zero. This problem covers concepts of multiplication, opposite numbers, and the zero property. Suitable for Grades 6-8.

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