Question
Use factoring by grouping to factor the following. \( y^{2}+a y+4 y+4 a=\square \)
Ask by Alexander Ford. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((y + a)(y + 4)\)
Solution
To factor the expression \( y^{2} + a y + 4 y + 4 a \) by grouping, follow these steps:
1. **Group the terms:**
\[
y^{2} + a y + 4 y + 4 a = (y^{2} + a y) + (4 y + 4 a)
\]
2. **Factor out the greatest common factor (GCF) from each group:**
- From the first group \( y^{2} + a y \), factor out \( y \):
\[
y(y + a)
\]
- From the second group \( 4 y + 4 a \), factor out \( 4 \):
\[
4(y + a)
\]
3. **Factor out the common binomial factor \( (y + a) \):**
\[
y(y + a) + 4(y + a) = (y + a)(y + 4)
\]
**Final Factored Form:**
\[
(y + a)(y + 4)
\]
Answer:
\((y + a)(y + 4)\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To factor the expression \( y^{2} + a y + 4 y + 4 a \) by grouping, first group the terms: \[ (y^{2} + a y) + (4 y + 4 a) \] Now, factor out the common factors in each group: \[ y(y + a) + 4(y + a) \] Next, notice that both groups contain the common binomial factor \( (y + a) \). Factor this out: \[ (y + a)(y + 4) \] So the factored form of the expression is: \[ (y + a)(y + 4) = \square \]
