Chapter 4.3, Problem 42WE

To determine

To multiply the polynomials.

Answer to Problem 42WE

The product of the expression is $a^3-b^3$

Explanation of Solution

Given information:

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

Calculation:

Arrange the work horizontally.

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

Therefore,

The product of the expression is $a^3-b^3$