Expanding the expression:
(a+1)(a+2)(a-3)-a(a-4)+= (a^2 + 2a + a + 2)(a-3) - (a^2 - 4a) + = (a^2 + 3a + 2)(a-3) - a^2 + 4a + = a^3 - 3a^2 + 3a^2 - 9a + 2a - 6 - a^2 + 4a + = a^3 - a^2 - 3a + 3a - 9 + 2a + 4a + = a^3 + 4a - 4
Therefore, the simplified expression is a^3 + 4a - 4.
Expanding the expression:
(a+1)(a+2)(a-3)-a(a-4)+
= (a^2 + 2a + a + 2)(a-3) - (a^2 - 4a) +
= (a^2 + 3a + 2)(a-3) - a^2 + 4a +
= a^3 - 3a^2 + 3a^2 - 9a + 2a - 6 - a^2 + 4a +
= a^3 - a^2 - 3a + 3a - 9 + 2a + 4a +
= a^3 + 4a - 4
Therefore, the simplified expression is a^3 + 4a - 4.