27a^3-1/9a^2-6a+1 Express in lowest terms?

Question

thanks

Answer 1

Recall the difference of cubes formula:

a^3-b^3 = (a-b)(a^2+ab+b^2)

So 27a^3-1 = (3a-1)(9a^2+3a+1)

Then

(27a^3-1) / (9a^2-6a+1)

= (3a-1)(9a^2+3a+1) / (9a^2-6a+1)

Nothing cancels.  It is already in lowest terms.