
Question content area top

Part 1

Factor the following expression by grouping.

xy minus x plus 2 y minus 2xy−x+2y−2

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Part 1

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

xy minus x plus 2 y minus 2xy−x+2y−2equals=enter your response here 

​(Factor completely.)

B.

The polynomial cannot be factored.

Let's factor the given expression by grouping. The expression is:

\[
xy - x + 2y - 2
\]

1. **Group the terms** in pairs:
   \[
   (xy - x) + (2y - 2)
   \]

2. **Factor out the common factor** from each group:
   \[
   x(y - 1) + 2(y - 1)
   \]

3. Notice that \((y - 1)\) is a common factor. So, factor \((y - 1)\) out:
   \[
   (x + 2)(y - 1)
   \]

Thus, the expression can be factored as:

\[
(x + 2)(y - 1)
\]

So, the correct choice is:

**A.** \( xy - x + 2y - 2 = (x + 2)(y - 1) \)

Would you like more details on the steps? Here are 5 related questions:

1. What is the significance of the common factor when grouping terms?
2. How can you verify that your factorization is correct?
3. Are there situations where grouping might not work?
4. How does the sign of each term affect the grouping process?
5. How do you factor expressions with more than four terms?

**Tip:** Always recheck your factorization by expanding the factors to ensure you return to the original expression.

Learn how to factor the expression xy - x + 2y - 2 using the method of grouping terms. Step-by-step solution provided, covering algebraic concepts such as factoring and grouping. Suitable for high school students.

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