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Chapter 0: Problem 56

Find each product. $$(x-1)^{3}$$

Short Answer

Expert verified
The product of \((x-1)^{3}\) is \(x^{3} - 3x^{2} + 3x - 1\).

Step by step solution

01

Apply the cubed binomial formula

We'll solve \((x-1)^{3}\) by using the formula for the cube of the binomial subtraction. This forces us to plug \(x\) in for \(a\) and \(1\) in for \(b\) in the general formula \((a-b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}\). After substituting, we get \(x^{3} - 3x^{2}*1 + 3x*1^{2} - 1^{3}\).
02

Simplify the obtained expression

Now, simplify the current expression by conducting the multiplications and raising to power where required. This leads to the form \(x^{3} - 3x^{2} + 3x - 1\)

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