Practicing Success
What is the value of $( k + \frac{1}{k}) ( k - \frac{1}{k}) ( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$ ? |
$k^{16}+\frac{1}{k^{16}}$ $k^{16}-\frac{1}{k^{16}}$ $k^{8}-\frac{1}{k^8}$ $k^{8}+\frac{1}{k^8}$ |
$k^{8}-\frac{1}{k^8}$ |
We know, a2 - b2 = (a+b)(a-b) $( k + \frac{1}{k}) ( k - \frac{1}{k}) ( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$ = $( k^2 - \frac{1}{k^2})( k^2 + \frac{1}{k^2}) ( k^4 + \frac{1}{k^4})$ = $( k^4 - \frac{1}{k^4})( k^4 + \frac{1}{k^4})$ = $k^{8}-\frac{1}{k^8}$ |