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

Question

4355 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-15T13:09:46

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

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

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

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

= $(4 x - y^{2}) ({(4 x)}^{2} + 4 x \times y^{2} + {(y^{2})}^{2})$ $(4x-y^2)((4x)^2+4x×y^2+(y^2)^2)$

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

How do you factor 64x^3 - y^664x3−y664x^3 - y^6?