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The image shows a mathematical expression followed by multiple-choice options for simplification or evaluation. The expression in question seems to be:

\[
6^n - 3 \times 2^n
\]
which is stated as "égal à" (equal to) with several answer choices.

The options provided are:
- a) \(2 \times 6^n\)
- b) \(2^n (3^n - 3)\)
- c) \(12^n\)
- d) \(3 \times 2^n (3^{n-1} - 1)\)

To solve the expression \(6^n - 3 \times 2^n\), we can break it down:

### Solution:

1. Factor \(6^n - 3 \times 2^n\):
   - Recall that \(6 = 2 \times 3\), so \(6^n = (2 \times 3)^n = 2^n \times 3^n\).
   - The expression becomes:
     \[
     6^n - 3 \times 2^n = 2^n \times 3^n - 3 \times 2^n
     \]
   - Factor out \(2^n\):
     \[
     2^n (3^n - 3)
     \]
   
2. This matches option **b)**: \(2^n (3^n - 3)\).

So, the correct answer is **b)**.

---

Would you like further details or have any questions? Here are some related questions you might consider:

1. How do you simplify other exponential expressions like \(a^n - b^n\)?
2. How would the answer change if the original expression was \(6^n + 3 \times 2^n\)?
3. What are common strategies for factoring exponential terms?
4. What are some examples of factoring binomials in exponential form?
5. How does factoring help simplify large expressions in algebra?

**Tip**: When simplifying, always look for common factors that can be factored out to reduce the complexity of the expression.

Simplify or evaluate the expression 6^n - 3 * 2^n

Learn how to simplify the exponential expression 6^n - 3 * 2^n by factoring common terms. Explore exponent rules and factoring strategies in this detailed solution for high school algebra students.

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