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Question
Simplify: a2b(a − b2) + ab2(4ab − 2a2) − a3b(1 − 2b)
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Solution
To simplify, we will use distributive law as follows:
\[a^2 b\left( a - b^2 \right) + a b^2 \left( 4ab - 2 a^2 \right) - a^3 b\left( 1 - 2b \right)\]
\[ = a^3 b - a^2 b^3 + 4 a^2 b^3 - 2 a^3 b^2 - a^3 b + 2 a^3 b^2 \]
\[ = a^3 b - a^3 b - a^2 b^3 + 4 a^2 b^3 - 2 a^3 b^2 + 2 a^3 b^2 \]
\[ = 3 a^2 b^3\]
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