Giải thích các bước giải:

A = (x-y)(x-2y)(x-3y)(x-4y) + $y^{4}$

= [ (x-y)(x-4y)] . [ (x-2y)(x-3y)] + $y^{4}$ 

=  ($x^{2}$ – 4xy – xy + 4$y^{2}$ ). ($x^{2}$ – 3xy – 2xy + 6$y^{2}$ ) + $y^{4}$ 

= ($x^{2}$ – 5xy + 4$y^{2}$ ) . ($x^{2}$ –  5xy + 6$y^{2}$) + $y^{4}$ 

= ($x^{2}$ – 5xy + 5$y^{2}$ – $y^{2}$ ) . ($x^{2}$ – 5xy + 5 $y^{2}$ + $y^{2}$ ) + $y^{4}$ 

= ($x^{2}$ – 5xy + 5$y^{2}$ )^2 – ($y^{2})^2$ + $y^{4}$ 

= ($x^{2}$ – 5xy + 5$y^{2}$ )^2 – $y^{4}$ + $y^{4}$ 

= ($x^{2}$ – 5xy + 5$y^{2}$ )^2

$\\$

`N=(x-y)(x-2y)(x-3y)(x-4y)+y^4`

`= (x^2 - 4xy - xy + 4y^2) (x^2 - 3xy - 2xy + 6y^2)+y^4`

`= (x^2 - 5xy + 4y^2) (x^2-5xy + 6y^2)+y^4`

Đặt `x^2-5xy+4y^2=t`

`= t (t+2y^2) + y^4`

`= t^2 + 2ty^2 + y^4`

`= t^2 + 2 . t . y^2 + (y^2)^2`

`= (t+y^2)^2`

`= (x^2-5xy + 4y^2+y^2)^2`

`=(x^2-5xy + 5y^2)^2`

`=>N` là SCP