Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 80

Subtract: $(-4m^2 + 3n^2 - 5n) - [(3m^2 - 5n^2 + 2n) + (-3m^2) + 4n^2]$

Since $3m^2$ and $−3m^2$ are like terms, add $−3m^2$ to $3m^2$ to get 0.

$−4m^2+3n^2−5n−(0−5n^2+2n+4n^2)$


Since $−5n^2$ and $4n^2$ are like terms, subtract $4n^2$ from $−5n^2$ to get $−n^2$.

$−4m^2+3n^2−5n−(−n^2+2n)$


Reorder the polynomial $−n^2+2n$ alphabetically from left to right, starting with the highest order term.

$−4m^2+3n^2−5n−(2n−n^2)$


Multiply $−1$ by each term inside the parentheses.

$−4m^2+3n^2−5n+n^2−2n$


Since $3n^2$ and $n^2$ are like terms, add $n^2$ to $3n^2$ to get $4n^2$.

$−4m^2+4n^2−5n−2n$


Since $−5n$ and $−2n$ are like terms, subtract $2n$ from $−5n$ to get $−7n$.

$−4m^2+4n^2−7n$