To simplify the given algebraic expression \((2m - 3n)(4n + 5m + 2)\), you can use the distributive property (FOIL method) to expand it:

\((2m - 3n)(4n + 5m + 2) = 2m(4n + 5m + 2) - 3n(4n + 5m + 2)\)

Now, distribute the terms:

\(2m * 4n + 2m * 5m + 2m * 2 - 3n * 4n - 3n * 5m - 3n * 2\)

Simplify each term:

\(8mn + 10m² + 4m - 12n² - 15mn - 6n\)

Now, collect like terms:

\((8mn - 15mn) + 10m² + 4m - 12n² - 6n\)

Combine the like terms:

\(-7mn + 10m² + 4m - 12n² - 6n\)

Now, you can see the coefficients of \(m²\), \(n²\), and \(mn\):

Coefficient of \(m²\): 10

Coefficient of \(n²\): -12

Coefficient of \(mn\): -7

So, the coefficients of \(m²\), \(n²\), and \(mn\) are 10, -12, and -7, respectively.

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