Simplifying and Factoring (n^3+4n^2+3n)(n^3+5n^2)
This expression represents the product of two polynomial expressions. To understand it better, we can simplify and factor it.
Simplifying the Expression

Factor out common terms:
 In the first polynomial, we can factor out 'n': n(n^2 + 4n + 3)
 In the second polynomial, we can factor out 'n^2': n^2(n + 5)

Rewrite the expression: The original expression now becomes: n(n^2 + 4n + 3) * n^2(n + 5)

Multiply the factored terms:
 n * n^2 = n^3
 (n^2 + 4n + 3) * (n + 5) = n^3 + 5n^2 + 4n^2 + 20n + 3n + 15 = n^3 + 9n^2 + 23n + 15
Therefore, the simplified expression is: n^3(n^3 + 9n^2 + 23n + 15)
Factoring the Expression
The simplified expression can be factored further.

Factor the trinomial: The trinomial (n^3 + 9n^2 + 23n + 15) can be factored by grouping:
 n^3 + 9n^2 + 23n + 15 = (n^3 + 9n^2) + (23n + 15)
 = n^2(n + 9) + (23n + 15)
Unfortunately, this trinomial cannot be factored further using simple methods.

Final factored form: The fully factored expression is: n^3(n^2(n + 9) + (23n + 15))
Conclusion
The expression (n^3+4n^2+3n)(n^3+5n^2) can be simplified and factored. While the trinomial (n^3 + 9n^2 + 23n + 15) cannot be factored further using simple methods, the final factored form is n^3(n^2(n + 9) + (23n + 15)).