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.

How do you factor 64a^3 - 8b^364a^3 - 8b^3?