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Chapter 0: Problem 17

Find each product. $$(2 x-3)\left(x^{2}-3 x+5\right)$$

Short Answer

Expert verified
The product of the given expressions is \(2x^3 - 9x^2 - 15\).

Step by step solution

01

Distribute First Terms

Multiply the first terms of each bracket together. This gives \(2x * x^2 = 2x^3\).
02

Distribute Outer and Inner Terms

Multiply the outer terms and inner terms of the brackets together. The outer terms are \(2x * -3x\), which gives \(-6x^2\), and the inner terms are \(-3 * x^2\), which gives \(-3x^2\). In total, this step gives us \(-6x^2 - 3x^2 = -9x^2\)
03

Distribute Last Terms

Multiply the last terms of each bracket together. This gives \(-3 * 5 = -15\)
04

Combine Results

Combine the results from the first three steps together. This gives \(2x^3 - 9x^2 - 15\)

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