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Chapter 0: Problem 25

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

Short Answer

Expert verified
The product \( (2x-3)(5x+3)\) is equal to \(10x^2 - 9x - 9\).

Step by step solution

01

- Multiply the First Terms

The first terms are \(2x\) and \(5x\). The product of these is \(10x^2\).
02

- Multiply the Outer Terms

The outer terms are \(2x\) and \(3\). The product of these is \(6x\).
03

- Multiply the Inner Terms

The inner terms are \(-3\) and \(5x\). The product of these yields \(-15x\).
04

- Multiply the Last Terms

The last terms are \(-3\) and \(3\). Multiplying these together gives \(-9\).
05

- Summarize and Simplify

Now add the products from each step: \(10x^2 + 6x - 15x - 9\). This simplifies to \(10x^2 - 9x - 9\) by combining like terms.

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