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How do you factor completely #a^3-10#?

1 Answer

Jul 13, 2017

#a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)#

Explanation:

#10# is not a perfect cube, but we can show its cube root as #root3 10# which is an irrational number.

The difference of cubes factorises as:
#x^3 -y^3 = (x-y)(x^2 +xy+y^2)#

#a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)#

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