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Descompuneti grupand convenabil termenii
a)[tex] x^{4} - x^{2} - 2x+2[/tex]
b)[tex] x^{4} + x^{3} +5x+5[/tex]
c)[tex] x^{3} + x^{2} y+ x^{2} - y^{2} [/tex]
d)[tex] x^{2}y + x y^{2} + x^{3}y -x y^{3} [/tex]
e)[tex]xy-x+5y-5 [/tex]
f)[tex]xy+x-y^{2} -y[/tex]
g)[tex]2x+2y+ x^{2} +xy- x^{2} y-x y^{2} [/tex]
h)[tex] x^{2} +x+xy+y- x^{3y- x^{2} y} [/tex]


Răspuns :

a)x²(x²-1)-2(x-1)=x²(x-1)(x+1)-2(x+1)=(x+1)[x²(x-1)-2]=(x+1)(x³-x²-2)
b)x³(x+1)+5(x+1)=(x+1)(x³+5)
c)x³+x²y+(x-y)(x+y)=x²(x+y)+(x-y)(x+y)=(x+y)(x²+x-y)
d)xy(x+y)+xy(x²-y²)=xy(x+y)+xy(x-y)(x+y)=xy(x+y)(1+x-y)
e)x(y-1)+5(y-1)=(y-1)(x+5)
f)x(y+1)-y(y+1)=(y+1)(x-y)
g)2(x+y)+x(x+y)-xy(x+y)=(x+y)(2+x-xy)