Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (x - 7)(y + 11) \)
Solution
To factor the expression \( xy + 11x - 7y - 77 \) by grouping, follow these steps:
1. **Group the terms:**
\[
(xy + 11x) + (-7y - 77)
\]
2. **Factor out the greatest common factor (GCF) from each group:**
- From the first group \( xy + 11x \), factor out \( x \):
\[
x(y + 11)
\]
- From the second group \( -7y - 77 \), factor out \( -7 \):
\[
-7(y + 11)
\]
3. **Factor out the common binomial factor \((y + 11)\):**
\[
(y + 11)(x - 7)
\]
**Final Factored Form:**
\[
(x - 7)(y + 11)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To factor by grouping the expression \(xy + 11x - 7y - 77\), we start by rearranging it: \((xy - 7y) + (11x - 77)\). Next, factor out the common terms in each group: \(y(x - 7) + 11(x - 7)\). Now, you see that \((x - 7)\) is a common factor; hence, we can factor it out: \((x - 7)(y + 11)\). The factored form is \((x - 7)(y + 11)\). This process not only simplifies the expression, but it also reveals useful insights into the relationships between the variables involved! And don’t forget, practice makes perfect—grab some similar expressions to try out your newfound skills!
