# Polynomial long division properties and simplify as long as possible

$$\frac{36 x^2-81 y^2}{216 x^3-729 y^3}$$

Answer will be in the form $\frac{A}{B}$ and the answer should be shortened as much as possible

• $36 x^2-81 y^2 = (6x)^2-(9y)^2$, $216 x^3-729 y^3 = (6x)^3-(9y)^3$. – njguliyev Sep 30 '13 at 9:36
• That's a good hint, @njguliyev. Make it an answer? – Cameron Buie Sep 30 '13 at 9:46

The big hint here is that: $$36x^2-81y^2=(6x)^2-(9y)^2\\216x^3-729y^3=(6x)^3-(9y)^3$$
• Well, $a^2-b^2=(a-b)(a+b)$. Have you ever seen that before? You've likely seen the way to factor $a^3-b^3,$ too. – Cameron Buie Sep 30 '13 at 11:32
• Not quite. Rather, it is $a^3-b^3=(a-b)(a^2+ab+b^2).$ – Cameron Buie Sep 30 '13 at 15:32