# Factorise x6 – y6

x6 – y6 = (x2)3 – (y2)3
= (x2 – y2)[(x2)2 + x2y2 +(y2)2]
= (x + y)(x – y)(x4 + x2y2 + y4)

(Here the third factor can be further factorised as shown)
= (x + y)(x – y)(x4 + 2x2y2 + y4 – x2y2)
= (x + y)(x – y)[(x2 + y2)2 – x2y2]
= (x + y)(x – y) (x2 + y2 + xy)(x2 + y2 – xy)

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