What is the value of $( k + \frac{1}{k}) ( k - \frac{1}{k}) ( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$ ?
Answer & explanation
Correct answer: option 3
We know,
a2 - b2 = (a+b)(a-b)
$( k + \frac{1}{k}) ( k - \frac{1}{k}) ( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$
= $( k^2 - \frac{1}{k^2})( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$
= $( k^4 - \frac{1}{k^4})( k^4 + \frac{1}{k^4})$
= $k^{8}-\frac{1}{k^8}$