Factor completely. \[ 4 x^{4}-100 x^{2} \]

To factor the expression \( 4x^{4} - 100x^{2} \), we can start by factoring out the greatest common factor (GCF) from both terms. Here, the GCF is \( 4x^{2} \): \[ 4x^{4} - 100x^{2} = 4x^{2}(x^{2} - 25) \] Next, notice that \( x^{2} - 25 \) is a difference of squares, which can be factored further: \[ x^{2} - 25 = (x - 5)(x + 5) \] Combining everything, the completely factored form of the original expression is: \[ 4x^{2}(x - 5)(x + 5) \] Feel free to double-check and confirm that all factors are correct!