To factor the expression \( 6xt - 2xy - 3t + y \), we can follow these steps:

### Step 1: Group terms
We can group terms in pairs to make factoring easier:
\[
(6xt - 2xy) - (3t - y)
\]

### Step 2: Factor out common terms from each group
In each group, we can factor out the common factors:
\[
2x(3t - y) - 1(3t - y)
\]

### Step 3: Factor out the common binomial
Now, \(3t - y\) is a common factor in both terms:
\[
(2x - 1)(3t - y)
\]

### Final Answer:
The factored form is:
\[
(2x - 1)(3t - y)
\]

Would you like more details or have any questions?

Here are five related questions for practice:
1. How do you factor \(4a + 8b - 2a - 4b\)?
2. Can you factor \(5xy - 10xz + 15yz\)?
3. How would you factor \(2m^2 - 3m - 2m + 3\)?
4. How do you approach factoring expressions with four terms, like \(3p - 3q + rp - rq\)?
5. How do you handle factoring when no common terms seem apparent at first?

**Tip:** When factoring expressions with four terms, look for common factors by grouping terms first.

Explore how to factor the expression 6xt - 2xy - 3t + y with a step-by-step guide. This problem demonstrates factoring by grouping and uses algebraic concepts suitable for Grades 9-10 students. Includes tips and practice questions.

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