How to factor x 3 1

Asked by maham237 @ in Mathematics viewed by 284 People

What is the factored form of
X^3-1

Answered by maham237 @


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)

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