Factor completely \[ 4 x^{2}-28 x y+49 y^{2} \]

To factor the expression \( 4x^2 - 28xy + 49y^2 \), we first look for a perfect square trinomial. The expression can be rewritten as follows: Notice that \( 4x^2 \) is the square of \( 2x \) and \( 49y^2 \) is the square of \( 7y \). The middle term \( -28xy \) can be derived from \( -2 \times 2x \times 7y \), indicating that the expression is indeed a perfect square: \[ 4x^2 - 28xy + 49y^2 = (2x - 7y)^2 \] Thus, the completely factored form of the expression is: \[ (2x - 7y)^2 \]