Verified answer

Hello,

In your situation, you should have used the well-known formulas: "Hello", "Please" and "Thanks"...

Anyway...

Let us set α=x–y to ease the solving:

(x – y)³ + (x – y – 2)³ + 8

  = α³ + (α – 2)³ + 2³

  = α³ + [(α – 2) + 2]×[(α – 2)² – 2(α – 2) + 2²] →→→ a³+b³=(a+b)(a²–ab+b²)

  = α³ + α[(α – 2)² – 2(α – 2) + 4]

  = α[α² + (α – 2)² – 2(α – 2) + 4]

  = α(α² + α² – 4α + 4 – 2α + 4 + 4)

  = α(2α² – 6α + 12)

  = 2α(α² – 3α + 6)

  = 2(x – y)[(x – y)² – 3(x – y) + 6]

No further factorization possible.

Regards,

Dragon.Jade :-)