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Chapter 0: Problem 34

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

Short Answer

Expert verified
The product of the binomials \( (2x+5) \) and \( (2x-5) \) is \( 4x^2 - 25 \).

Step by step solution

01

Multiply First Terms

First, multiply the first terms in each binomial. For our problem, this means multiplying \(2x\) by \(2x\), which yields \(4x^2\).
02

Multiply Outside Terms

Next, multiply the outside terms in the binomial expression. In this case, it involves multiplying \(2x\) (from the first binomial) and \(-5\) (from the second binomial), resulting in \(-10x\).
03

Multiply Inside Terms

Then, multiply the inside terms. This involves multiplying \(5\) (from the first binomial) and \(2x\) (from the second binomial), yielding \(10x\).
04

Multiply Last Terms

Finally, multiply the last terms in each binomial. Here, we multiply \(5\) by \(-5\), giving \(-25\).
05

Combine Like Terms

Combine the results from previous steps. We have \(4x^2\), \(-10x\), \(10x\), and \(-25\). The \(-10x\) and \(10x\) cancel each other out, so the final expression is \(4x^2 - 25\).

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