How do you factor #216m^3+1/64#?

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Answer 1 · 2015-06-02T17:53:35

#216m^3 + 1/64#

#=(6m)^3+(1/4)^3#

#=((6m)+(1/4))((6m)^2-(6m)(1/4)+(1/4)^2)#

#=(6m+1/4)(36m^2-(3m)/2+1/16)#

...using the sum of cubes identity

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

There are no simpler factors with real coefficients.