Problem 84 - College Algebra Essentials

Question

Perform the indicated operation or operations. $$(5 x+2 y)^{2}-(5 x-2 y)^{2}$$

Step-by-Step Solution

Answer

The result of the indicated operation is \(40xy\).

Step 1: Expand the brackets

First we need to expand each square (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b². Therefore, \((5x + 2y)^{2}\) expands to \(25x^{2} + 20xy + 4y^{2}\) and \((5x - 2y)^{2}\) expands to \(25x^{2} - 20xy + 4y^{2}\).

Step 2: Subtract the expansions

Now subtract the second square \((25x^{2} - 20xy + 4y^{2})\) from the first square \((25x^{2} + 20xy + 4y^{2})\) as per the initial equation. This yields \(40xy\).