Chapter 4.2, Problem 41WE

To determine

To simplify: the polynomial $(u^3-3u^{2}v+2u{v}^2)+(3u^{2}v-2u{v}^2-v^3)$

Answer to Problem 41WE

The required answer is: $u^3-v^3$

Explanation of Solution

Given information:

The given polynomial: $(u^3-3u^{2}v+2u{v}^2)+(3u^{2}v-2u{v}^2-v^3)$

Calculation:

  $(u^3-3u^{2}v+2u{v}^2)+(3u^{2}v-2u{v}^2-v^3)=u^3-3u^{2}v+2u{v}^2+3u^{2}v-2u{v}^2-v^3$

(Removing the bracket)

  $=u^3+(-3u^{2}v+3u^{2}v)+(2u{v}^2-2u{v}^2)-v^3$

(Commutative Property of addition)

  $\begin{array}{l}=u^3+0+0-v^3\\ =u^3-v^3\end{array}$

(Simplify)