Use factoring by grouping to factor the following. \( y^{2}+a y+4 y+4 a=\square \)

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: \((y + a)(y + 4)\)