How do you factor #27x^3+8#?

1 Answer
Monzur R.
Oct 5, 2016

#27x^3+8=(3x)^3+2^3=(3x+2)(9x^2-6x+4)#

Explanation:

Think of #27x^3# as #(3x)^3# and #8# as #2^3#.

This is a sum of cubes and we can apply the sum of cubes formula: #a^3 + b^3 = (a + b) (a^2 − ab + b^2 )#.

Substituting #a# with #3x# and #b# with #3# into the formula yields: #x^3 + 27 = (3x+2)(9x^2-6x+4)#

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