Question

(a-1/a)(a+1/a)(a²+1/a²)(a⁴+1/a⁴) =​

Answer 1

(a+1/a)(a-1/a)(a²+1/a²)(a⁴+1/a⁴)

=[(a+1/a)(a-1/a)](a²+1/a²)(a⁴+1/a⁴)

=[a²-(1/a)²](a²+1/a²)(a⁴+1/a⁴)

=[(a²-1/a²)(a²+1/a²)](a⁴+1/a⁴)

= [(a²)²-(1/a²)²](a⁴+1/a⁴)

= (a⁴-1/a⁴)(a⁴+1/a⁴)

= (a⁴)²-(1/a⁴)²

Therefore,

(a+1/a)(a-1/a)(a²+1/a²)(a⁴+1/a⁴) =

Answer 2

Answer:

$a^8 - \frac{1}{a^8}$

Step-by-step explanation:

⇒ $(a - \frac{1}{a} ) ( a + \frac{1}{a} ) (a^2 + \frac{1}{a^2}) (a^4 + \frac{1}{a^4} )$

⇒ $(a^2 - \frac{1}{a^2} ) (a^2 + \frac{1}{a^2} ) (a^4 + \frac{1}{a^4} )$      [ $(a+b) (a-b) = a^2 - b^2$]

⇒ $(a^4 - \frac{1}{a^4}) (a^4 + \frac{1}{a^4} )$

⇒ $a^8 - \frac{1}{a^8}$