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-9c^{2}+9c^{2}+6cd+d^{2}-d^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3c+d\right)^{2}.
6cd+d^{2}-d^{2}
Combine -9c^{2} and 9c^{2} to get 0.
6cd
Combine d^{2} and -d^{2} to get 0.
-9c^{2}+9c^{2}+6cd+d^{2}-d^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3c+d\right)^{2}.
6cd+d^{2}-d^{2}
Combine -9c^{2} and 9c^{2} to get 0.
6cd
Combine d^{2} and -d^{2} to get 0.