Question

Simplify:  a²b(a³ − a + 1) − ab(a⁴ − 2a² + 2a) − b (a³ − a² − 1)

Answer 1

To simplify, we will use distributive law as follows:​

\[a^2 b\left( a^3 - a + 1 \right) - ab\left( a^4 - 2 a^2 + 2a \right) - b\left( a^3 - a^2 - 1 \right)\]

\[ = a^5 b - a^3 b + a^2 b - a^5 b + 2 a^3 b - 2 a^2 b - a^3 b + a^2 b + b\]

\[ = a^5 b - a^5 b - a^3 b + 2 a^3 b - a^3 b + a^2 b - 2 a^2 b + a^2 b + b\]

\[ = b\]