To factor the expression \( 10ab - 6b + 35a - 21 \) by grouping, follow these steps:

### Step 1: Group terms
Group the terms in pairs to prepare for factoring:
\[
(10ab - 6b) + (35a - 21)
\]

### Step 2: Factor out the greatest common factor (GCF) from each group
- From the first group \( 10ab - 6b \), the GCF is \( 2b \):
\[
10ab - 6b = 2b(5a - 3)
\]
- From the second group \( 35a - 21 \), the GCF is \( 7 \):
\[
35a - 21 = 7(5a - 3)
\]

### Step 3: Factor out the common binomial factor
Now the expression is:
\[
2b(5a - 3) + 7(5a - 3)
\]
Since both terms have the common factor \( (5a - 3) \), factor it out:
\[
(5a - 3)(2b + 7)
\]

Thus, the factored form of \( 10ab - 6b + 35a - 21 \) is:
\[
(5a - 3)(2b + 7)
\]

Would you like more details or have any questions about this?

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Here are five related questions to deepen understanding:
1. How do you determine the greatest common factor (GCF) in a binomial?
2. What is the importance of grouping when factoring polynomials?
3. Can you try factoring a similar expression like \( 12xy - 8y + 18x - 12 \)?
4. How would this process change for a quadratic expression?
5. How do you check if your factored result is correct?

**Tip:** Always check your factored expression by expanding it to ensure it matches the original expression.

10ab - 6b + 35a - 21 factored with grouping

Learn how to factor the algebraic expression 10ab - 6b + 35a - 21 using the grouping method. This solution breaks down factoring by grouping and identifying the greatest common factor (GCF), suitable for students in Grades 9-10.

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