Problem 56 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(x^{3} - 3x^{2}*1 + 3x*1^{2} - 1^{3}\).

Step 2: Simplify the obtained expression

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