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\( 14x + 49 = 7(2x + 7) \)
Solución
It looks like you're working with the expression:
\[ 14x + 49 \]
**Factorizing the Expression:**
To factorize \( 14x + 49 \), you can look for the greatest common factor (GCF) of the two terms.
1. **Identify the GCF:**
- The GCF of 14 and 49 is **7**.
2. **Factor out the GCF:**
\[
14x + 49 = 7(2x) + 7(7) = 7(2x + 7)
\]
**Final Factored Form:**
\[
14x + 49 = 7(2x + 7)
\]
**Verification:**
To ensure the factorization is correct, you can expand the factored form:
\[
7(2x + 7) = 7 \times 2x + 7 \times 7 = 14x + 49
\]
This matches the original expression, confirming that the factorization is accurate.
**Summary:**
\[
14x + 49 = 7(2x + 7)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
Did you know that the expression \( 14x + 49 \) can actually be factored? Yup! You can pull out a common factor from both terms, which in this case is 7. So, it can be rewritten as \( 7(2x + 7) \). Factoring like this can make solving equations or graphing much simpler! In real-world applications, expressions like \( 14x + 49 \) often pop up in various fields like finance, where they can represent profits as a function of sales (x). By understanding how to manipulate and factor these expressions, you can better analyze trends and forecasts in business—turning math into money-making strategies!
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