How do you factor the sum or difference of two cubes #x^3-27#?

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Answer 1 · 2015-04-09T06:08:28

The factor of #x^3-27=(x-3)(x^2+3x+9)#

Beginning Equation:

#x^3-27#

This is a case of factoring difference of cubes.

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

For #(x^3-27)#:

#a^3=x^3#

#a=root(3)(x^3)=x#

#b^3=27#

#b=root(3)(27)=3#

#a=x, b=3#

#(x^3-27)=(x-3)(x^2+(x*3)+9)#=

#(x-3)(x^2+3x+9)#