Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 82

Solve $[-(4m^2 - 8m + 4m^3) - (3m^2 + 2m + 5m^3)] + m^2$
Reorder the polynomial 4m2−8m+4m3 alphabetically from left to right, starting with the highest order term.


$−(4m^3+4m^2−8m)−(3m^2+2m+5m^3)+m^2$


Reorder the polynomial $3m^2+2m+5m^3$ alphabetically from left to right, starting with the highest order term.

$−(4m^3+4m^2−8m)−(5m^3+3m^2+2m)+m^2$


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

$−4m^3−4m^2+8m−(5m^3+3m^2+2m)+m^2$


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

$−4m^3−4m^2+8m−5m^3−3m^2−2m+m^2$


Since $−4m^3$ and $−5m^3$ are like terms, subtract $5m^3$ from $−4m^3$ to get $−9m^3$.

$−9m^3−4m^2+8m−3m^2−2m+m^2$


Since $-4m^2$ and $−3m^2$ are like terms, subtract $3m^2$ from $−4m^2$ to get $−7m^2$.

$−9m^3−7m^2+8m−2m+m^2$


Since $−7m^2$ and $m^2$ are like terms, subtract $m^2$ from $−7m^2$ to get $−6m^2$.

$−9m^3−6m^2+8m−2m$


Since $8m$ and $−2m$ are like terms, add $−2m$ to $8m$ to get $6m$.

$−9m^3−6m^2+6m$