factor the expression
-216x^{3}+1 = (-6x)^{3}+1
This is a "sum of cubes" (since 1 = 1^{3}), which has the form:
a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})
In this problem, a = -6x and b = 1
-216x^{3} + 1 = (-6x + 1)(36x^{2} + 6x + 1)
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