How do you factor #64a^3 - 8b^3#?

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Answer 1 · 2015-05-30T12:36:36

This is a difference of cubes...

#64a^3-8b^3 = (4a)^3 - (2b)^3#

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

So

#(4a)^3 - (2b)^3 = ((4a)-(2b))((4a)^2+(4a)(2b)+(2b)^2)#

#=(4a-2b)(16a^2+8ab+4b^2)#

#=8(2a-b)(4a^2+2ab+b^2)#

The are no simpler factorings with real coefficients.