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Algebra Level 3

{a+a2+a3+=56a2+a3+a4+=2566b+b2+b3+=65b2+b3+b4+=3655\large{ \begin{cases} a+a^2+a^3+\cdots=\dfrac{5}{6} \\ a^2+a^3+a^4+\cdots=\dfrac{25}{66} \\ b+b^2+b^3+\cdots=\dfrac{6}{5} \\ b^2+b^3+b^4+\cdots=\dfrac{36}{55} \end{cases}}

Given the above, find a2b2a^2-b^2.

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