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9a^{2}-6ab+b^{2}-\left(a-3b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-b\right)^{2}.
9a^{2}-6ab+b^{2}-\left(a^{2}-6ab+9b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.
9a^{2}-6ab+b^{2}-a^{2}+6ab-9b^{2}
To find the opposite of a^{2}-6ab+9b^{2}, find the opposite of each term.
8a^{2}-6ab+b^{2}+6ab-9b^{2}
Combine 9a^{2} and -a^{2} to get 8a^{2}.
8a^{2}+b^{2}-9b^{2}
Combine -6ab and 6ab to get 0.
8a^{2}-8b^{2}
Combine b^{2} and -9b^{2} to get -8b^{2}.
9a^{2}-6ab+b^{2}-\left(a-3b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-b\right)^{2}.
9a^{2}-6ab+b^{2}-\left(a^{2}-6ab+9b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.
9a^{2}-6ab+b^{2}-a^{2}+6ab-9b^{2}
To find the opposite of a^{2}-6ab+9b^{2}, find the opposite of each term.
8a^{2}-6ab+b^{2}+6ab-9b^{2}
Combine 9a^{2} and -a^{2} to get 8a^{2}.
8a^{2}+b^{2}-9b^{2}
Combine -6ab and 6ab to get 0.
8a^{2}-8b^{2}
Combine b^{2} and -9b^{2} to get -8b^{2}.