Factor the expression completely. \[ 100 x^{4}-30 x^{2} \]

To factor the expression completely, we start by looking for a common factor in both terms. Here, both \(100x^4\) and \(-30x^2\) share a common factor of \(10x^2\). So we can factor out \(10x^2\): \[ 100x^4 - 30x^2 = 10x^2(10x^2 - 3) \] Next, we need to check if the expression inside the parentheses \(10x^2 - 3\) can be factored further. This is a difference of squares form, however, it cannot be factored over the integers. Therefore, the completely factored expression is: \[ 10x^2(10x^2 - 3) \]