How do you factor $1000x^3-1$ ?

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Answer 1 · 2018-06-30T07:30:36

$1000x^3-1 = (10x-1)(100x^2+10x+1)$

Note that both $1000x^3 = (10x)^3$ and $1 = 1^3$ are perfect cubes.

So we can immediately use the difference of cubes identity:

$A^3-B^3 = (A-B)(A^2+AB+B^2)$

to find:

$1000x^3-1 = (10x)^3-1^3$

$color(white)(1000x^3-1) = (10x-1)((10x)^2+10x+1)$

$color(white)(1000x^3-1) = (10x-1)(100x^2+10x+1)$

How do you factor 1000x^3-11000x^3-1?