Question

СРОЧНО:ДАЮ 80 БАЛЛОВ

Решите тождество

Answer 1

$(a-x)(a+x)(a^2+x^2)(a^4+x^4)=(a^2-x^2)(a^2+x^2)(a^4+x^4)=(a^4-x^4)(a^4+x^4)=a^8-x^8$

Формула - $(a-b)(a+b)=a^2-b^2$

Answer 2

$a^8-x^8=(a^4)^2-(x^4)^2=\\\\=(a^4-x^4)(a^4+x^4)=\Big ((a^2)^2-(x^2)^2\Big )\Big (a^4+x^4\Big )=\\\\=(a^2-x^2)(a^2+x^2)(a^4+x^4)=\\\\=(a-x)(a+x)(a^2+x^2)(a^4+x^4)\\\\\\\boxed {a^8-x^8=(a^4+x^4)(a^2+x^2)(a+x)(a-x)}$