How do you factor #27a^3-64b^3#?

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Answer 1 · 2016-01-08T12:10:10

#27a^3-64b^3=(3a-4b)(9a^2+12ab+16b^2)#

Remembering that:

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

we can try to write

#27a^3-64b^3#

like a difference of cubes

#27a^3-64b^3=3^3a^3-2^6b^3=3^3a^3-(2^2)^3b^3=#
#(3a)^3-4^3b^3=(3a)^3-(4b)^3#

Now we can apply the rule:

#27a^3-64b^3=(3a)^3-(4b)^3=#
#=(3a-4b)((3a)^2+12ab+(4b)^2)#
#=(3a-4b)(9a^2+12ab+16b^2)#