To factorize the expression \( 5b + 15b^2 \), we start by identifying the common factors in each term.

1. **Identify the Greatest Common Factor (GCF):**  
   The terms are \( 5b \) and \( 15b^2 \). The GCF of 5 and 15 is 5, and the lowest power of \( b \) between \( b \) and \( b^2 \) is \( b \).

   So, the GCF is \( 5b \).

2. **Factor Out the GCF:**  
   We can rewrite the expression as:
   \[
   5b + 15b^2 = 5b(1 + 3b)
   \]

Thus, the completely factorized form of the expression is:
\[
5b(1 + 3b)
\]

Would you like further details or have any questions?

Here are some related questions to consider:

1. How do we determine the greatest common factor in algebraic expressions?
2. How would we factor \( 10b + 20b^2 \)?
3. What happens if there are no common factors in an expression?
4. How does factoring help simplify expressions in algebra?
5. Can you factorize \( 5b + 15b^2 + 10b^3 \)?

**Tip:** Always look for the greatest common factor in each term before attempting other factoring methods.

Learn how to factorize the algebraic expression 5b + 15b^2 by finding the Greatest Common Factor (GCF). Follow a step-by-step approach suitable for students in Grades 7-9 to understand factoring basics in algebra.

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