How do you factor #27x^3+64#?

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Answer 1 · 2015-04-12T05:03:26

When factorising the sum of cubes, we use the formula
#a^3+b^3=(a+b)(a^2-ab+b^2)#.

In this case of #27x3+64#,
#27x^3 = a^3#
#64=b^3#

Find #a#:
#27x^3 = a^3#
#root3 (27x^3) = root3 (a^3)#
#3x = a#

Find #b#:
#64=b^3#
#root3 64 = root3 (b^3)#
#4 = b#

Substitute #a=3x# and #b=4# into #(a+b)(a^2-ab+b^2)#

#(3x+4)((3x)^2 - (3x xx4) + 4^2)#

= #(3x+4)(9x^2 - 12x + 16)#

#(3x+4)(9x^2 - 12x + 16)# is the factorised form of #27x3+64#