To determine the equivalnet expression solve each of the given options.
For option A.
![\begin{gathered} b+2(b+2)=b+2(3b) \\ =b+6b \\ =7b \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/3nn4x1a4rmtgnozcb0gqui72kvujqjh5ye.png)
For option B.
![3b+b=4b](https://img.qammunity.org/2023/formulas/mathematics/high-school/f3pp2m70sgdzy9mtpozn78mwslp3jm1jpf.png)
Option B results in 4b, so 3b + b is equivalent to 4b.
For option C.
![\begin{gathered} 2(2b)=2\cdot2b \\ =4b \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bkdzhd3b1s6sapr1pdks1ssh3uj96kcgub.png)
Option C results in 4b, so 2(2b) is equivalent to 4b.
Option B and option C are correct.