Question

problem 1 multiplying a monomial and a trinomial got it? what is a simpler form of $5n(3n^3 - n^2 + 8)$?

Explanation:

Step1: Apply distributive property

Multiply \(5n\) with each term inside the parentheses: \(5n\times3n^{3}-5n\times n^{2}+5n\times8\)

Step2: Simplify each product

For \(5n\times3n^{3}\), use \(a^{m}\times a^{n}=a^{m + n}\): \(15n^{4}\)
For \(5n\times n^{2}\): \(5n^{3}\)
For \(5n\times8\): \(40n\)
Combine the results: \(15n^{4}-5n^{3}+40n\)

Answer:

\(15n^{4}-5n^{3}+40n\)