Докажите тождество. 1)(a-b)(a+b)(a^2+b^2)=a^4-b^4. 2)(a^4+b^4)(a^2+b^2(a+b)(a-b)=a^8-b-^8

Question

Докажите тождество. 1)(a-b)(a+b)(a^2+b^2)=a^4-b^4. 2)(a^4+b^4)(a^2+b^2(a+b)(a-b)=a^8-b-^8

Answer 1

1)
(а-b)(a+b)(a²+b²)=a⁴-b⁴
(a²-b²)(a²+b²)=a⁴-b⁴
a⁴-b⁴=a⁴-b⁴
2)
(a⁴+b⁴)(a²+b²)(a+b)(a-b)=a^8-b^8
(a^6+b^6)(a²-b²)=a^8-b^8
a^8-b^8=a^8-b^8