Find the product. (5x+2y)^2 (5x+2y)^2= square

To find the product \((5x + 2y)^2\), we use the **square of a binomial formula**:<br /><br />\[<br />(a + b)^2 = a^2 + 2ab + b^2<br />\]<br /><br />Here, \(a = 5x\) and \(b = 2y\). Substituting these into the formula:<br /><br />\[<br />(5x + 2y)^2 = (5x)^2 + 2(5x)(2y) + (2y)^2<br />\]<br /><br />### Step-by-step calculation:<br />1. Square the first term: <br /> \[<br /> (5x)^2 = 25x^2<br /> \]<br /><br />2. Multiply the two terms and double it:<br /> \[<br /> 2(5x)(2y) = 20xy<br /> \]<br /><br />3. Square the second term:<br /> \[<br /> (2y)^2 = 4y^2<br /> \]<br /><br />### Combine all terms:<br />\[<br />(5x + 2y)^2 = 25x^2 + 20xy + 4y^2<br />\]<br /><br />### Final Answer:<br />\[<br />(5x + 2y)^2 = 25x^2 + 20xy + 4y^2<br />\]