Solve $x^{3} - 8$

Step-by-step solution

Step 1 · Recognise cubes
$x^{3} - 8 = x^{3} - 2^{3}$
8 is 2³, so the difference-of-cubes pattern applies.
Step 2 · Difference of cubes
$(x - 2) (x^{2} + 2 x + 4)$
a³ − b³ = (a − b)(a² + ab + b²); the quadratic factor is irreducible over the reals.

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$x^{2} - 9$