No, the method used to solve the given equation is not "factoring by grouping." Factoring by grouping is a technique typically used to factor polynomials, especially those with four terms, by grouping terms in pairs and factoring out common factors within each group.

In your equation:

\[ 2.36y = 214x + 12.6x - 72y \]

we combined like terms and isolated the variable, which is a straightforward method for solving linear equations. Factoring by grouping involves different steps, typically used in situations like the following example:

Given the polynomial:
\[ ax + ay + bx + by \]

We can group and factor as:
\[ (ax + ay) + (bx + by) \]
\[ a(x + y) + b(x + y) \]
\[ (a + b)(x + y) \]

Factoring by grouping would be used for expressions like this, not for the linear equation we solved.

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

Here are some related questions that could help you understand this topic better:

1. What is the purpose of factoring by grouping?
2. Can you provide an example where factoring by grouping is applicable?
3. How do you determine when to use factoring by grouping?
4. What are some other factoring techniques for polynomials?
5. How does solving linear equations differ from factoring polynomials?
6. What are some common mistakes to avoid when factoring by grouping?
7. How do you check if your factorization by grouping is correct?
8. What are the steps involved in solving quadratic equations?

**Tip:** Factoring by grouping is a valuable technique for breaking down complex polynomials, but always make sure to use the appropriate method for the type of equation or expression you are working with.

Explore the differences between linear equations and factoring by grouping. Learn when to use each method with examples and step-by-step explanations. Suitable for students in Grades 7-9.

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