Question

Descompuneti (a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)

Answer 1

Notam P=(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)

Daca a=b => P=2a*2a^2*2a^4*2a^8*2a^16*2a^32=64a^63.
Daca a diferit de b:
(a-b)P=(a-b)(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)=(a^2-b^2)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)=(a^4-b^4)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)=...=(a^32-b^32)(a^32+b^32)=a^64-b^64. => P=(a^64-b^64)/(a-b).