Answer:
[tex]\begin{equation*} (4-r)(16+4r+r^2) \end{equation*}[/tex]
Explanation:
Given:
[tex]64-r^3[/tex]
To factor the above binomial completely, we'll first rewrite it as seen below;
[tex]64-r^3=4^3-r^3[/tex]
Recall the difference cubes formula below;
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
If we compare both expressions, we can see that a = 4 and b = r, so we we'll have;
[tex]4^3-r^3=(4-r)(4^2+4r+r^2)=(4-r)(16+4r+r^2)[/tex]
