How do you factor #8k^3 + 1#?

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Answer 1 · 2016-02-11T17:39:28

#(2k+1)(4k^2-2k+1)#

This is the factorization of perfect cubes.

The pattern for factoring perfect cubes is
#(a+b)(a^2-ab+b^2)#
or
#(a-b)(a^2+ab+b^2)#
The pattern is dependent upon the sign between the cubes.

a = the cubic factor of the first term
b = the cubic root of the second term

(first term, second term) (first term squared, first term x second term, second term squared.

The pattern of the pattern of the signs follows the SOAP rule
S - Same Sign
O - Opposite Sign
AP - Always Positive

(Same Sign) (Opposite Sign, Always Positive)

#8k^3 + 1#
The cubic factor of #8k^3# is 2k
The cubic factor of 1 is 1

#a = 2k#
#b = 1#

#(2k + 1)((2k)^2-(2k)(1)+(1)^2)#
#(2k + 1)(4k^2-2k+1)#