Factor. \( 49 s^{4}-64 s^{2} d^{4} \) \( 49 s^{4}-64 s^{2} d^{4}=\square \) \( ( \) Factor completely.)

To factor the expression \( 49 s^{4} - 64 s^{2} d^{4} \), start by recognizing that this is a difference of squares. We can rewrite it as: \[ (7s^{2})^{2} - (8d^{2})^{2} \] Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we have: \[ (7s^{2} - 8d^{2})(7s^{2} + 8d^{2}) \] Next, let's see if we can factor any further. The first term \( 7s^{2} - 8d^{2} \) is akin to a difference of squares if we consider it as \( ( \sqrt{7}s - 2\sqrt{2}d)( \sqrt{7}s + 2\sqrt{2}d) \) but not fully factorizable over the integers. Thus, the complete factorization of \( 49 s^{4} - 64 s^{2} d^{4} \) is: \[ (7s^{2} - 8d^{2})(7s^{2} + 8d^{2}) \] There's your answer! 🎉