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Chapter 0: Problem 77

Find each product. $$[5 y-(2 x+3)][5 y+(2 x+3)]$$

Short Answer

Expert verified
The result of the product is \(25y^2 - 4x^2 - 12x - 9\)

Step by step solution

01

Recognize the Difference of Squares

First thing to recognize is that the given formula \([5 y-(2 x+3)][5 y+(2 x+3)]\) is a difference of two squares. Because it is in the format of \((a+b)(a-b)\)
02

Apply the Difference of Squares Formula

Apply the difference of squares formula \(a^2 - b^2\) to our expression where \(a = 5y\) and \(b = 2x + 3\). So, \(a^2\) would be \((5y)^2\) and \(b^2\) would be \((2x + 3)^2\)
03

Simplify the Result

Finally simplify the result, \((5y)^2 = 25y^2\) and \((2x + 3)^2 = 4x^2 + 12x + 9\) yielding the final expression \(25y^2 - (4x^2 + 12x + 9) = 25y^2 - 4x^2 - 12x - 9\)

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