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The expression provided is \(14x + 7\). To factor this expression completely, we need to find the greatest common factor (GCF) of the terms.

1. **Identify the GCF:** The GCF of 14 and 7 is 7.
2. **Factor out the GCF:** We can factor out 7 from the expression.

So, \(14x + 7\) can be factored as:
\[
14x + 7 = 7(2x + 1)
\]

To check by multiplying, distribute the 7 back into the expression:
\[
7(2x + 1) = 7 \times 2x + 7 \times 1 = 14x + 7
\]
This confirms that the factorization is correct.

Would you like more details on this, or do you have any questions?

Here are 5 related questions to further explore:
1. How do you factor expressions with more than two terms?
2. What is the difference between factoring completely and partially?
3. Can you factor a quadratic expression like \(x^2 + 5x + 6\)?
4. How would you factor the expression \(14x - 7\)?
5. What are common mistakes to avoid when factoring expressions?

**Tip:** Always double-check your factorization by distributing back to ensure the original expression is obtained.

Learn how to factor the expression 14x + 7 by identifying the greatest common factor (GCF) and applying the distributive property. Suitable for students in Grades 6-8.

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