How do you factor the difference of two cubes #x^3 - 216#?

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Answer 1 · 2015-04-09T04:07:24

Remember this formula for factorizing difference of 2 cubes:
#a^3−b^3=(a−b)(a^2+ab+b^2)#

In #x^3-216#,

#a^3=x^3#
#b^3=216#

#a= root3(x^3)# = #x#
#b=root3(216)#= #6#

Substitute #a=x # , #b=6 # into the formula of #(a-b)(a^2+ab+b^2)#

#(x-6)##(x^2# + (#6#x#x#) + #6^2##)# = #(x-6)##(x^2# + #6x#+ #36)#

#(x-6)##(x^2# + #6x#+ #36)# is the factorized form of #x^3-216#