Problem 34 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Multiply First Terms

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

Step 2: 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 \(-10x\).

Step 3: Multiply Inside Terms

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

Step 4: Multiply Last Terms

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

Step 5: 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 \(4x^2 - 25\).