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

1 Answer
Jun 30, 2018

Answer:

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

Explanation:

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)#