Question

What is the factored form of
X^3-1

Answer 1

Notice how both terms are perfect cubes. You can factor using the difference of cubes formula:


`a^3-b^3=(a-b)(a^2+ab+b^2) \\ \\ x^3-1 = x^3- 1^3 = (x-1)(x^2+x+1)`

The factored form of x³ - 1 is (x - 1)(x² + x + 1).

Answer 2

keeping in mind that

1² = 1
1³ = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰ = 1


`\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2)\\\\ -------------------------------\\\\ x^3-1\implies x^3-1^3\implies (x-1)(x^2+1x+1^2) \\\\\\ (x-1)(x^2+x+1)`