Find the product. (4-5y)^2 (4-5y)^2= square (Simplify your answer.)

To simplify \( (4 - 5y)^2 \), we use the **square of a binomial formula**:<br /><br />\[<br />(a - b)^2 = a^2 - 2ab + b^2<br />\]<br /><br />Here, \( a = 4 \) and \( b = 5y \). Substituting into the formula:<br /><br />\[<br />(4 - 5y)^2 = 4^2 - 2(4)(5y) + (5y)^2<br />\]<br /><br />### Step-by-step calculation:<br />1. \( 4^2 = 16 \)<br />2. \( -2(4)(5y) = -40y \)<br />3. \( (5y)^2 = 25y^2 \)<br /><br />Now combine these terms:<br /><br />\[<br />(4 - 5y)^2 = 16 - 40y + 25y^2<br />\]<br /><br />### Final Answer:<br />\[<br />(4 - 5y)^2 = 25y^2 - 40y + 16<br />\]