Multiply using special product methods. \[ (5 x-y)^{2} \]

Using the special product method for squaring a binomial, we can expand \( (5x - y)^{2} \) using the formula \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = 5x \) and \( b = y \). We calculate: 1. \( a^{2} = (5x)^{2} = 25x^{2} \) 2. \( 2ab = 2 \cdot (5x) \cdot y = 10xy \) 3. \( b^{2} = y^{2} \) Putting it all together: \[ (5x - y)^{2} = 25x^{2} - 10xy + y^{2} \] And there you have it, the expanded form is \( 25x^{2} - 10xy + y^{2} \)!