Chapter 4.3, Problem 44WE

To determine

To multiply the polynomials.

Answer to Problem 44WE

The product of the expression is $a^4+b^4$

Explanation of Solution

Given information:

The given expression is $\left(a+b\right)\left(a^3-a^{2}b+a{b}^2-b^3\right)$

Calculation:

Arrange the work horizontally.

  $\begin{array}{l}\left(a+b\right)\left(a^3-a^{2}b+a{b}^2-b^3\right)=a\left(a^3-a^{2}b+a{b}^2-b^3\right)+b\left(a^3-a^{2}b+a{b}^2-b^3\right)\\ =a^4-a^{3}b+a^2{b}^2-a{b}^3+a^{3}b-a^2{b}^2+a{b}^3+b^4\\ =a^4+b^4\end{array}$

Therefore,

The product of the expression is $a^4+b^4$