Question

Prove the identity.
a^8-b^8=(a-b)(a+b)(a^2+b^2)(a^4+b^4)

Answer 1

Start from the right side
RS = (a-b)(a+b)(a^2+b^2)(a^4+b^4)
First, use difference of two squares to expand (a-b)(a+b),
ie. (a-b)(a+b) = (a^2 - b^2)
So, you get
RS = (a-b)(a+b)(a^2+b^2)(a^4+b^4)
= (a^2 - b^2))(a^2+b^2)(a^4+b^4)
Use the same trick to expand it. Can you do it now?

Answer 2

Yes Thanks!

Answer 3

Welcome :)

Answer 4

You can also start from the left though
a^8-b^8 = (a^4)^2 - (b^4)^2
= (a^4 - b^4)(a^4 + b^4)
= [ (a^2)^2 - (b^2)^2 ] (a^4 + b^4)
Then, difference of two squares again...