512a^3+125 divided by or over 64a^2 -25

Darkend asked Sep 7, 2022

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Darkend asked Sep 7, 2022

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23 votes

Answer:

(64a^2 -40a +25)/(8a -5)

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.

$(512a^3+125)/(64a^2-25)=((8a)^3+5^3)/((8a)^2-5^2)=((8a+5)((8a)^2-(8a)(5)+5^2)/((8a+5)(8a-5))\\\\=\boxed{(64a^2-40a+25)/(8a-5)}$

Jack Carlisle answered Sep 13, 2022

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