To simplify the expression (a+1)(a+2)(a+3), we can use the distributive property and multiply each term in the first set of parentheses by each term in the second set of parentheses, and then multiply the result by the third term:

(a+1)(a+2)(a+3) = (a(a+2))(a+3) + (1(a+2))(a+3) = (a^2 + 2a)(a+3) + (a+2)(a+3) = a^3 + 3a^2 + 2a^2 + 6a + a^2 + 3a + 2a + 6 = a^3 + 6a^2 + 11a + 6

Therefore, the simplified expression is a^3 + 6a^2 + 11a + 6.