Chapter 8.7, Problem 51PPE

To determine

To calculate:The factor of $64r^6-144r^3+81$

Answer to Problem 51PPE

  ${(8r^3-9)}^2$

Explanation of Solution

Given information:The expression $64r^6-144r^3+81$

Calculation:

  $\begin{array}{l}64r^6-144r^3+81\\ $ ={(8r^3)}^2-2(8r^3)(9)+{(9)}^2$$ ={(8r^3-9)}^2[\because {(a-b)}^2=a^2-2ab+b^2]$\end{array}$

Thus, $64r^6-144r^3+81={(8r^3-9)}^2$