Problem 128 - College Algebra

Question

Explain how to factor \(x^{3}+1\)

Step-by-Step Solution

Answer

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

Step 1: Identify the Values of a and b

We first need to identify the values of 'a' and 'b' from the equation \(x^{3}+1\). Here, \(a=x\) and \(b=1\).

Step 2: Apply the Sum of Cubes Formula

Next, apply the sum of cubes formula: \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\). With the values of 'a' and 'b' substituted, the formula equates to \(x^{3}+1^{3}=(x+1)(x^{2}-x*1+1^{2})\).

Step 3: Simplify the Formula

Simplifying the equation further, we get \(x^{3}+1=(x+1)(x^{2}-x+1)\).