Question

Factorise: (a-b)^5+(b-c)^5+(c-a)^5

Answer 1

Answer:

=−5a4b+5a4c+10a3b2−10a3c2−10a2b3+10a2c3+5ab4−5ac4−5b4c+10b3c2−10b2c3+5bc4

Step-by-step explanation:

Let's simplify step-by-step.

(a−b)5+(b−c)5+(c−a)5

Distribute:

=a5+−5a4b+10a3b2+−10a2b3+5ab4+−b5+b5+−5b4c+10b3c2+−10b2c3+5bc4+−c5+−a5+5a4c+−10a3c2+10a2c3+−5ac4+c5

Combine Like Terms:

=a5+−5a4b+10a3b2+−10a2b3+5ab4+−b5+b5+−5b4c+10b3c2+−10b2c3+5bc4+−c5+−a5+5a4c+−10a3c2+10a2c3+−5ac4+c5

=(a5+−a5)+(−5a4b)+(5a4c)+(10a3b2)+(−10a3c2)+(−10a2b3)+(10a2c3)+(5ab4)+(−5ac4)+(−b5+b5)+(−5b4c)+(10b3c2)+(−10b2c3)+(5bc4)+(−c5+c5)

=−5a4b+5a4c+10a3b2+−10a3c2+−10a2b3+10a2c3+5ab4+−5ac4+−5b4c+10b3c2+−10b2c3+5bc4

Answer 2

Answer:

First answer is correct!!

Step-by-step explanation: