Problem 34 - College Algebra

Question

Find each product. $$(2 x+5)(2 x-5)$$

Step-by-Step Solution

Answer

The product of \((2x + 5)(2x - 5)\) is \(4x^2 - 25\).

Step 1: Recognizing the pattern

The given expression, \((2x + 5)(2x - 5)\), it is noted to be in the form \(a^2 - b^2\). Here, \(a = 2x\) and \(b = 5\). Therefore, it can be written as \((2x)^2 - (5)^2\).

Step 2: Square the terms

In this step, we square each term. So, \((2x)^2 = 4x^2\) and \((5)^2 = 25\). The expression now becomes \(4x^2 - 25\) .

Step 3: Writing the final answer

No further simplification is possible, thus \(4x^2 - 25\) is the final answer.