The final result should be \(m^{6}n^{2} - 3m^{3}n - 40\).
In order to multiply any polynomials, use the pattern FOIL (which stands for first, outer, inner, last). You multiply what they ask you to at each step.
First - The first terms in both parenthesis.
\(m^{3}n * m^{3}n = m^{6}n^{2}\)
Outer - The terms on the outside of both parenthesis.
\(m^{3}n * -5 = -5m^{3}n\)
Inner - The terms on the inside of both parenthesis.
\(m^{3}n * 8 = 8m^{3}n\)
Last - the last numbers in each parenthesis.
8 * - 5 = - 40
Now we put all the answers together and simplify like terms,
\(m^{6}n^{2} + -5m^{3}n + 8m^{3}n - 40\)
\(m^{6}n^{2} - 3m^{3}n - 40\)
