Question

Polynomials
find the product of (x-1/x)(x+1/x)(x^2+1/x^2)(x^4+1/x^4)

Answer 1

$hey \: friend \: here \: is \: your \: answer. \: plese \: mark \: my \: answer \: as \: the \: brillianist \: answer$
( x - 1/x ) ( x + 1/x ) ( x² + 1 / x²) ( x^4 + 1 / x^4 )
$using \: (a + b)(a - b) = {a}^{2} - {b}^{2}$
=[ ( x - 1/x ) ( x + 1/x ) ] ( x² + 1 / x²) ( x^4 + 1 / x^4 )
= [ ( x - 1 ) ( x + 1 ) / x * x ] ( x² + 1 / x²) ( x^4 + 1 / x^4 )
= [ x² - 1² / x² ] ( x² + 1 / x²) ( x^4 + 1 / x^4 )
= ( x² - 1 / x² ) ( x² + 1 / x²) ( x^4 + 1 / x^4 )
= [ ( x² - 1 / x² ) ( x² + 1 / x²) ] ( x^4 + 1 / x^4 )
= [ ( x²-1 ) ( x²+1 ) / x² * x² ] ( x^4 + 1 / x^4 )
= [ (x²)² -1²/x^4 ] ( x^4 + 1 / x^4 )
= ( x^4 - 1 / x^4 ) ( x^4 + 1 / x^4 )
= [ ( x^4 - 1 ) ( x^4 + 1 ) / x^4 * x^4 )
= [ (x^4)² -1² / x^8 ]
= ( x^8 - 1 / x^8 )
= x^8 - 1 / x^8
Hope it helps. Please mark my answer as the brillianist answer.