Question

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$a) \: \: x {}^{4} - {x}^{2} - 2x + 2 \\ b) \: {x}^{2} y + x {y}^{2} + {x}^{ 3 }y - x {y}^{3}$

Answer 1

Rezolvarea in atasament.

Answer 2

   
[tex]\displaystyle\\ a)\\ x^4-x^2- 2x + 2 =\\ =x^2(x^2-1)-2(x-1)=\\ =x^2(x+1)(x-1)-2(x-1)=\\ =(x-1)[x^2(x+1)-2]=\\ =(x-1)[x^3+x^2-2]=\\ =(x-1)[x^3+x^2-1-1]=\\ =(x-1)[x^3-1+x^2-1]=\\ =(x-1)[(x-1)(x^2+x+1)+(x-1)(x+1)]=\\ =(x-1)(x-1)(x^2+x+1+x+1)=\\ =\boxed{(x-1)^2(x^2+2x+2)}[/tex]


[tex]\displaystyle\\ b)\\ x^2y + xy^2+x^3y - xy^3=\\ =xy[(x + y)+(x^2-y^2)]=\\ =xy[(x + y)+(x+y)(x-y)]=\\ =\boxed{xy(x + y)(1+x-y)} [/tex]