Question
Factor the following expression by grouping. \[ x y+8 x+7 y+56 \] Select the correct choice below and, if necessary, fill in the answer box to A. \( x y+8 x+7 y+56=\square \) ) (Factor completely) B. The polynomial cannot be factored.
Ask by Li Knight. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x y + 8 x + 7 y + 56 = (y + 8)(x + 7) \)
Solution
To factor the expression \( x y + 8 x + 7 y + 56 \) by grouping, follow these steps:
1. **Group the terms:**
\[
(x y + 8 x) + (7 y + 56)
\]
2. **Factor out the greatest common factor (GCF) from each group:**
- From the first group \( x y + 8 x \), factor out \( x \):
\[
x(y + 8)
\]
- From the second group \( 7 y + 56 \), factor out \( 7 \):
\[
7(y + 8)
\]
3. **Factor out the common binomial factor \( (y + 8) \):**
\[
x(y + 8) + 7(y + 8) = (y + 8)(x + 7)
\]
**Answer:**
**A.**
\[
x y + 8 x + 7 y + 56 = (y + 8)(x + 7)
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To factor the expression \( xy + 8x + 7y + 56 \) by grouping, let's first rearrange it as \( (xy + 7y) + (8x + 56) \). Factoring each group, we get \( y(x + 7) + 8(x + 7) \). Now, we see that \( (x + 7) \) is a common factor, so we can rewrite the expression as \( (x + 7)(y + 8) \). So, the correct choice is: A. \( xy + 8x + 7y + 56 = (x + 7)(y + 8) \) (Factor completely)
