How do you factor #27a^3-8#?

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Answer 1 · 2018-04-07T18:02:47

#27a^3-8=color(red)((3a-2)(9a^2+6a+4))#

We have a difference of cubes:

#27a^3-8#

#=(3a)^3-2^3#

To factor a difference of cubes, use the formula:

#a^3-b^3=(a-b)(a^2+ab+b^2)#

#(3a)^3-2^3=color(red)((3a-2)(9a^2+6a+4))#

This cannot be factored any further using rational numbers, so this is the fully factored form.