SOLUTION: i really need help with this one: Given that, a=b+1 Prove that {{{(a+b)(a^2+b^2)(a^4+b^4)= a^8-b^8}}} Thanks in advance.

Algebra ->  Expressions-with-variables -> SOLUTION: i really need help with this one: Given that, a=b+1 Prove that {{{(a+b)(a^2+b^2)(a^4+b^4)= a^8-b^8}}} Thanks in advance.      Log On


   

Question 120379: i really need help with this one:
Given that, a=b+1
Prove that %28a%2Bb%29%28a%5E2%2Bb%5E2%29%28a%5E4%2Bb%5E4%29=+a%5E8-b%5E8
Thanks in advance.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
factoring a^8-b^8 (difference of two squares) gives (a^4+b^4)(a^4-b^4)

factoring a^4-b^4 (difference of two squares) gives (a^2+b^2)(a^2-b^2)

factoring a^2-b^2 (difference of two squares) gives (a+b)(a-b)

substitution gives a-b=b+1-b=1

so a^8-b^8=(a^4+b^4)(a^2+b^2)(a+b)(1)