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How do you factor #x^3+1?

1 Answer

May 6, 2015

$x^{3} + 1 = x^{3} + 1^{3}$ $x^3+1 = x^3 + 1^3$

The sum of cubes identity tells us that :

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $color(blue)(a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

Hence $x^{3} + 1^{3} = (x + 1) (x^{2} - (x \cdot 1) + 1^{2})$ $x^3 + 1^3 = (x + 1)(x^2 - (x*1) + 1^2)$

$= (x + 1) (x^{2} - x + 1)$ $= color(green)((x + 1)(x^2 - x + 1)$

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