How i can factor #8(a^(6n))+27(b^(3m))# ?

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Answer 1 · 2018-03-16T13:57:11

See below.

Using the identity

#u^3+v^3 = (u-v)(u^2-u v + v^2)#

#(2a^(2n))^3+(3b^m)^3 = (2a^(2n)-3b^m)((2a^(2n))^2-2a^(2n)3b^m+(3b^m)^2) = (2 a^(2 n) + 3 b^m) (4 a^(4 n) - 6 a^(2 n) b^m + 9 b^(2 m))#

How i can factor #8*(a^(6n))+27*(b^(3m))# ?