Question

To simplyfy

[(A^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3]
/ [(a-b)^3 +(b-c)^3+(c-a)^3]

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ {( {a}^{2} - {b}^{2} )}^{3} + {( {b}^{2} - {c}^{2} )}^{3} + {( {c}^{2} - {a}^{2} )}^{3} }{ {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} }$

Using the identity :

${( {a}^{m}) }^{n} = {a}^{mn}$

$\frac{ {a}^{6} - {b}^{6} + {b}^{6} - {c}^{6} + {c}^{6} - {a}^{6} }{ {a}^{3} - {b}^{3} + {b}^{3} - {c}^{3} + {c}^{3} - {a}^{3} } \\ \\ = \frac{0}{0} \\ \\ = 0$


Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺

Answer 2

Hiiiiiii friends.....,.
here is your answer.......
hope it help you