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Chapter 0: Problem 84

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

Short Answer

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

Step by step solution

01

Expand the brackets

First we need to expand each square (a+b)虏 = a虏 + 2ab + b虏 and (a-b)虏 = a虏 - 2ab + b虏. Therefore, \((5x + 2y)^{2}\) expands to \(25x^{2} + 20xy + 4y^{2}\) and \((5x - 2y)^{2}\) expands to \(25x^{2} - 20xy + 4y^{2}\).
02

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 \(40xy\).

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