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.

How do you factor 216m^3+1/64216m^3+1/64?