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Chapter 0: Problem 25

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

Short Answer

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

Step by step solution

01

Multiply the First Terms

First, multiply the first terms (the 'F' in FOIL) of each binomial, i.e., \(2x\) and \(5x\), getting \(10x^2\).
02

Multiply the Outer Terms

Next, multiply the outer terms (the 'O' in FOIL), i.e., \(2x\) and \(3\), getting \(6x\).
03

Multiply the Inner Terms

Then multiply the inner terms (the 'I' in FOIL), i.e., \(-3\) and \(5x\), getting \(-15x\).
04

Multiply the Last Terms

Finally, multiply the last terms (the 'L' in FOIL), i.e., \(-3\) and \(3\), getting \(-9\).
05

Add the Products

Add together the products obtained from the previous steps: \(10x^2 + 6x - 15x - 9\). The final result will be \(10x^2 - 9x - 9\).

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