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AB\left(A^{2}-1\right)
Factor out AB.
\left(A-1\right)\left(A+1\right)
Consider A^{2}-1. Rewrite A^{2}-1 as A^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
AB\left(A-1\right)\left(A+1\right)
Rewrite the complete factored expression.