https://file.aiquickdraw.com/mathbot/file/17289658831276im8ojy6.jpg

Let's solve the problem shown in the image.

---

### **Problem:**
You need to factor the expression:
\[
2a^2b - 3a + 10ab^2 - 15b
\]

---

### **Solution:**
We'll use **grouping** to factor the expression step-by-step.

1. Group the terms:
   \[
   (2a^2b + 10ab^2) - (3a + 15b)
   \]

2. Factor out the greatest common factor (GCF) from each group:
   - From \(2a^2b + 10ab^2\), the GCF is \(2ab\):
     \[
     2ab(a + 5b)
     \]
   - From \(-3a - 15b\), the GCF is \(-3\):
     \[
     -3(a + 5b)
     \]

3. Now, factor out the common binomial \((a + 5b)\):
   \[
   (a + 5b)(2ab - 3)
   \]

---

### **Answer:**
The correct factored form is:
\[
\boxed{B) (a + 5b)(2ab - 3)}
\]

---

Do you need any further clarifications?

### 5 Related Questions:
1. What is the method of grouping, and when is it useful?
2. How do you identify the greatest common factor (GCF) of algebraic terms?
3. Can every polynomial be factored using grouping?
4. What are alternative strategies for factoring four-term polynomials?
5. How do negative signs affect factorization?

### Tip:
When using grouping, always check that the binomials formed in each group are identical—this ensures the grouping method is working correctly.

Factor the expression: 2a^2b - 3a + 10ab^2 - 15b

Learn how to factor the polynomial 2a^2b - 3a + 10ab^2 - 15b using the grouping method. This detailed step-by-step guide explores key algebraic concepts such as factoring and finding the greatest common factor. Suitable for students in Grades 8-10.

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