Problem 25 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1 - Multiply the First Terms

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

Step 2 - Multiply the Outer Terms

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

Step 3 - Multiply the Inner Terms

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

Step 4 - Multiply the Last Terms

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

Step 5 - 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.