Answer:
(64a^2 -40a +25)/(8a -5)
Step-by-step explanation:
The quotient is found by using the "special form" factoring of the sum of cubes and the difference of squares. Factors (8a+5) cancel.
[tex]\dfrac{512a^3+125}{64a^2-25}=\dfrac{(8a)^3+5^3}{(8a)^2-5^2}=\dfrac{(8a+5)((8a)^2-(8a)(5)+5^2}{(8a+5)(8a-5)}\\\\=\boxed{\dfrac{64a^2-40a+25}{8a-5}}[/tex]
