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a^{2}-b^{2}-2\left(a-b\right)^{2}
Consider \left(a-b\right)\left(a+b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
a^{2}-b^{2}-2\left(a^{2}-2ab+b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.
a^{2}-b^{2}-2a^{2}+4ab-2b^{2}
Use the distributive property to multiply -2 by a^{2}-2ab+b^{2}.
-a^{2}-b^{2}+4ab-2b^{2}
Combine a^{2} and -2a^{2} to get -a^{2}.
-a^{2}-3b^{2}+4ab
Combine -b^{2} and -2b^{2} to get -3b^{2}.
a^{2}-b^{2}-2\left(a-b\right)^{2}
Consider \left(a-b\right)\left(a+b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
a^{2}-b^{2}-2\left(a^{2}-2ab+b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.
a^{2}-b^{2}-2a^{2}+4ab-2b^{2}
Use the distributive property to multiply -2 by a^{2}-2ab+b^{2}.
-a^{2}-b^{2}+4ab-2b^{2}
Combine a^{2} and -2a^{2} to get -a^{2}.
-a^{2}-3b^{2}+4ab
Combine -b^{2} and -2b^{2} to get -3b^{2}.