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4a^{2}-12ab+9b^{2}-\left(2a+3b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-3b\right)^{2}.
4a^{2}-12ab+9b^{2}-\left(4a^{2}+12ab+9b^{2}\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+3b\right)^{2}.
4a^{2}-12ab+9b^{2}-4a^{2}-12ab-9b^{2}
To find the opposite of 4a^{2}+12ab+9b^{2}, find the opposite of each term.
-12ab+9b^{2}-12ab-9b^{2}
Combine 4a^{2} and -4a^{2} to get 0.
-24ab+9b^{2}-9b^{2}
Combine -12ab and -12ab to get -24ab.
-24ab
Combine 9b^{2} and -9b^{2} to get 0.
4a^{2}-12ab+9b^{2}-\left(2a+3b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-3b\right)^{2}.
4a^{2}-12ab+9b^{2}-\left(4a^{2}+12ab+9b^{2}\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+3b\right)^{2}.
4a^{2}-12ab+9b^{2}-4a^{2}-12ab-9b^{2}
To find the opposite of 4a^{2}+12ab+9b^{2}, find the opposite of each term.
-12ab+9b^{2}-12ab-9b^{2}
Combine 4a^{2} and -4a^{2} to get 0.
-24ab+9b^{2}-9b^{2}
Combine -12ab and -12ab to get -24ab.
-24ab
Combine 9b^{2} and -9b^{2} to get 0.