How do you factor $64x^3 - y^6$ ?

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Answer 1 · 2018-06-15T13:09:46

$64x^3-y^6=(4x-y^2)(16x^2+4xy^2+y^4)$

As $64x^3-y^6$ can be written as $(4x)^3-(y^2)^3$ , we can use the identity

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Hence $64x^3-y^6=(4x)^3-(y^2)^3$

= $(4x-y^2)((4x)^2+4x×y^2+(y^2)^2)$

= $(4x-y^2)(16x^2+4xy^2+y^4)$

How do you factor 64x^3 - y^664x^3 - y^6?