Question

FIND THE PRODUCT [ALGEBRA]
(X_1)(X+1)(x2+1)(x4+1)

Answer 1

$Use:(a-b)(a+b)=a^2-b^2\ \ \ (*)\\\\============================\\\\\underbrace{(x-1)(x+1)}_{(*)}(x^2+1)(x^4+1)=\underbrace{(x^2-1)(x^2+1)}_{(*)}(x^4+1)\\\\=\underbrace{(x^4-1)(x^4+1)}_{(*)}=x^8-1$



$\left(a^n\right)^m=a^{n\times m}$

Answer 2

(x-1)×(x+1)=x²-1
(x²-1)×(x²+1) = x^4-1
(x^4-1)×(x^4+1) = x^8-1
  solved using the identity:
(a+b)×(a-b)=a²-b²