Question

final exam - requires respondus lockdown browser
started: dec 10 at 8:50pm
quiz instructions
question 23
perform the indicated operation.
$(9m + 2)(5m^2 + m - 6)$
\\( 45m^3 + 19m^2 - 52m - 12 \\)
\\( 45m^3 + 1m^2 - 52m - 12 \\)
\\( 14m^2 - 52m - 12 \\)
\\( 45m^3 - 52m - 12 \\)

Explanation:

Step1: Apply distributive property

Multiply \(9m\) by each term in \(5m^2 + m - 6\) and \(2\) by each term in \(5m^2 + m - 6\):
\(9m\times5m^2 = 45m^3\), \(9m\times m = 9m^2\), \(9m\times(-6)= - 54m\)
\(2\times5m^2 = 10m^2\), \(2\times m = 2m\), \(2\times(-6)= - 12\)

Step2: Combine like terms

Combine the \(m^2\) terms: \(9m^2+10m^2 = 19m^2\)
Combine the \(m\) terms: \(-54m + 2m=-52m\)
The constant term is \(-12\)
So the result is \(45m^3 + 19m^2-52m - 12\)

Answer:

\(45m^3 + 19m^2-52m - 12\) (the first option among the given choices)