Q. 60 - Intermediate Algebra

Question

In the following exercises, add or subtract the polynomials. 

$\left(a^3-2a^{2}b\right)+\left(a{b}^2+b^3\right)-\left(3a^{2}b+4a{b}^2\right)$

Step-by-Step Solution

Answer

Hence,

$\left(a^3-2a^{2}b\right)+\left(a{b}^2+b^3\right)-\left(3a^{2}b+4a{b}^2\right)=a^3-5a^{2}b-3a{b}^2+b^3$

Step 1. Given information

$\begin{array}{l}\text{The given expressions is}\\ \left(a^3-2a^{2}b\right)+\left(a{b}^2+b^3\right)-\left(3a^{2}b+4a{b}^2\right)\\ \text{We have to add or subtract the polynomials as applicable.}\end{array}$

Step 2. Simplify

$\begin{array}{l}\Rightarrow \left(a^3-2a^{2}b\right)+\left(a{b}^2+b^3\right)-\left(3a^{2}b+4a{b}^2\right)\\ =a^3-2a^{2}b+a{b}^2+b^3-3a^{2}b-4a{b}^2\left[\text{Rewrite without parentheses}\right]\\ =a^3-2a^{2}b-3a^{2}b+a{b}^2-4a{b}^2+b^3\left[\text{Combine the like terms}\right]\\ =a^3-5a^{2}b-3a{b}^2+b^3\left[\text{Simplify}\right]\end{array}$