How do you factor #16ax^3 + 54ay^3#?

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Answer 1 · 2015-06-07T20:55:19

#16ax^3+54ay^3#

#=2a(8x^3+27y^3)#

#=2a((2x)^3+(3y)^3)#

#=2a(2x+3y)((2x)^2-(2x)(3y)+(3y)^2)#

#=2a(2x+3y)(4x^2-6xy+9y^2)#

...using the sum of cubes identity:

#A^3+B^3 = (A+B)(A^2-AB+B^2)#

There are no simpler factors with real coefficients.