Factor by grouping. \( 25 y^{3}+15 y^{2}+15 y+9 \)

To factor by grouping, we can first group the terms in pairs: \[ (25y^3 + 15y^2) + (15y + 9) \] Now, we factor out the common factors in each group: From the first group \( 25y^3 + 15y^2 \), we can factor out \( 5y^2 \): \[ 5y^2(5y + 3) \] From the second group \( 15y + 9 \), we can factor out \( 3 \): \[ 3(5y + 3) \] Now we have: \[ 5y^2(5y + 3) + 3(5y + 3) \] Since \( (5y + 3) \) is a common factor, we can factor that out as well: \[ (5y + 3)(5y^2 + 3) \] So, the fully factored form is: \[ (5y + 3)(5y^2 + 3) \]