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

Step 1 ：Identify the quadratic in the form \(ax^2 + bx + c\): \(4w^4 - 100w^2\)

Step 2 ：Notice that this is a difference of squares, which can be factored as \((a^2 - b^2) = (a - b)(a + b)\)

Step 3 ：Here, \(a = 2w^2\) and \(b = 10w\)

Step 4 ：Factor the expression as \((2w^2 - 10w)(2w^2 + 10w)\)

Step 5 ：Notice that each term in the first factor has a common factor of \(2w\), and each term in the second factor has a common factor of \(2w\)

Step 6 ：Factor out these common factors to get \(2w(w - 5)(2w(w + 5))\)