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Question
Simplify: a2b(a3 − a + 1) − ab(a4 − 2a2 + 2a) − b (a3 − a2 − 1)
Solution
To simplify, we will use distributive law as follows:
\[a^2 b\left( a^3 - a + 1 \right) - ab\left( a^4 - 2 a^2 + 2a \right) - b\left( a^3 - a^2 - 1 \right)\]
\[ = a^5 b - a^3 b + a^2 b - a^5 b + 2 a^3 b - 2 a^2 b - a^3 b + a^2 b + b\]
\[ = a^5 b - a^5 b - a^3 b + 2 a^3 b - a^3 b + a^2 b - 2 a^2 b + a^2 b + b\]
\[ = b\]
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