Question

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

Answer 1

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)