Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 84

Solve $[2p - (3p - 6)] - [(5p - (8 - 9p)) + 4p]$
Multiply $-1$ by each term inside the parentheses.
$2p−(3p−6)−(5p+9p−8+4p)$


Since $5p$ and $9p$ are like terms, add $9p$ to $5p$ to get $14p$.

$2p−(3p−6)−(14p−8+4p)$


Since $14p$ and $4p$ are like terms, add $4p$ to $14p$ to get $18p$.

$2p−(3p−6)−(18p−8)$


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

$2p+6−3p−(18p−8)$


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

$2p+6−3p+8−18p$


Since $2p$ and $−3p$ are like terms, add $−3p$ to $2p$ to get $−p$.

$−p+6+8−18p$


Since $−p$ and $−18p$ are like terms, subtract $18p$ from $−p$ to get $−19p$.

$−19p+6+8$


Add 8 to 6 to get 14.

$−19p+14$


Reorder the polynomial $−19p+14$ alphabetically from left to right, starting with the highest order term.

$14−19p$