Evaluate
a^{3}+4ab-8b^{3}-8b^{2}
Expand
a^{3}+4ab-8b^{3}-8b^{2}
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a^{2}-4b^{2}+a^{3}-8b^{3}-\left(a^{2}-4ab+4b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2b\right)^{2}.
a^{2}-4b^{2}+a^{3}-8b^{3}-a^{2}+4ab-4b^{2}
To find the opposite of a^{2}-4ab+4b^{2}, find the opposite of each term.
-4b^{2}+a^{3}-8b^{3}+4ab-4b^{2}
Combine a^{2} and -a^{2} to get 0.
-8b^{2}+a^{3}-8b^{3}+4ab
Combine -4b^{2} and -4b^{2} to get -8b^{2}.
a^{2}-4b^{2}+a^{3}-8b^{3}-\left(a^{2}-4ab+4b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2b\right)^{2}.
a^{2}-4b^{2}+a^{3}-8b^{3}-a^{2}+4ab-4b^{2}
To find the opposite of a^{2}-4ab+4b^{2}, find the opposite of each term.
-4b^{2}+a^{3}-8b^{3}+4ab-4b^{2}
Combine a^{2} and -a^{2} to get 0.
-8b^{2}+a^{3}-8b^{3}+4ab
Combine -4b^{2} and -4b^{2} to get -8b^{2}.
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