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Chapter 0: Problem 18

Find each product. $$(2 x-1)\left(x^{2}-4 x+3\right)$$

Short Answer

Expert verified
So, the product of \((2x-1)\) and \((x^{2}-4x+3)\) is \(2x^{3} - 9x^{2} + 10x -3\).

Step by step solution

01

Distribute the first term

First, distribute the term \(2x\) to each term in the binomial \((x^{2}-4x+3)\). This gives the three terms: \(2x * x^{2} = 2x^{3}\), \(2x * -4x = -8x^{2}\), and \(2x * 3 = 6x\).
02

Distribute the second term

Next, distribute the term \(-1\) to each term in the binomial \((x^{2}-4x+3)\). This gives the terms: \(-1 * x^{2} = -x^{2}\), \(-1 * -4x = 4x\), and \(-1 * 3 = -3\).
03

Combine like terms

Finally, combine the like terms from the first and second step. Thus getting \(2x^{3} - 8x^{2} + 6x -x^{2} + 4x-3\), which simplifies to \(2x^{3} - 9x^{2} + 10x -3\).

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