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

1. Recognize that the expression \( (5x - y)^2 \) is a squared binomial. The formula for a squared binomial is: \[ (a - b)^2 = a^2 - 2ab + b^2 \] 2. Identify \( a \) and \( b \) in the expression: \[ a = 5x \quad \text{and} \quad b = y \] 3. Substitute \( a \) and \( b \) into the formula: \[ (5x - y)^2 = (5x)^2 - 2(5x)(y) + y^2 \] 4. Compute each term: - First term: \[ (5x)^2 = 25x^2 \] - Second term: \[ -2(5x)(y) = -10xy \] - Third term: \[ y^2 = y^2 \] 5. Combine the terms to obtain the final answer: \[ (5x - y)^2 = 25x^2 - 10xy + y^2 \]