How do you factor $100a^6-64b^8$ ?

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Answer 1 · 2015-07-13T00:09:37

$100a^6-64b^8 = 4(5a^3-4b^4)(5a^3+4b^4)$

This is a difference of squares, but first separate out the common scalar factor $4$ :

$100a^6-64b^8$

$= 4(25a^6-16b^8)$

$= 4((5a^3)^2-(4b^4)^2)$

$= 4(5a^3-4b^4)(5a^3+4b^4)$

using the difference of squares identity:

$A^2-B^2 = (A-B)(A+B)$

with $A = 5a^3$ and $B=4b^4$

How do you factor 100a^6-64b^8100a^6-64b^8?