Question

1. factor the following expression: $x^3 - 1$

Explanation:

Step1: Recall the difference of cubes formula

The formula for factoring the difference of cubes is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\).

Step2: Identify \(a\) and \(b\) in the given expression

In the expression \(x^3-1\), we have \(a = x\) and \(b = 1\) since \(1=1^3\).

Step3: Apply the difference of cubes formula

Substitute \(a=x\) and \(b = 1\) into the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\).
We get \((x - 1)(x^2+x\times1 + 1^2)=(x - 1)(x^2+x + 1)\).

Answer:

\((x - 1)(x^2+x + 1)\)