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x2 + y2 - x2y2 + xy - x - y
=(x2-x2y2)+(y2-y)+(xy-x) 
=x2(1-y)(1+y)-y(1-y)-x(1-y)
=(1-y)(x2+x2y-x-y)
=(1-y)[(x2-y)+(x2-x)]
=(1-y)[y(x-1)(x+1)+x(x-1)]
=(1-y)(x-1)(xy+x+y)

x2 + y2 - x2y2 + xy - x - y = (x2-x) + (y2-y) + (-x2y2 + xy) = x(x+1) + y(y+1) + xy(xy+1) = ( x+ y+ xy)( x + 1 + y + 1 + xy + 1)

\(x^2+y^2-x^2y^2+xy-x-y\)

\(=\left(x^2-x\right)+\left(y^2-y\right)+ \left(-x^2y^2+xy\right)\)

\(=x\left(x+1\right)+y\left(y+1\right)+xy\left(xy+1\right)\)

\(=\left(x+y+xy\right)\left(x+1+y+1+xy+1\right)\)

a) \(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)

\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)

\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)

a) Ta có: \(x^4+2x^3-4x-4\)

\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)

\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)

\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)

\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)

d) Ta có: \(a^3+b^3+c^3-3abc\)

\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)

\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)

\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)

Ta có: M = x3 + xy + y2 – x2y2 – 2 và N = x2y2 + 5 – y2

⇒ M + N = (x3 + xy + y2 – x2y2 – 2) + (x2y2 + 5 – y2)

= x3 + xy + y2 – x2y2 – 2 + x2y2 + 5 – y2

= x3 + (– x2y2 + x2y2) + (y2 – y2) + xy + (– 2 + 5)

= x3 + 0 + 0 + xy + 3

= x3 + xy + 3.

a) (x - y)(x + y + 3).                    b) (x + y - 2xy)(2 + y + 2xy).

c) x 2 (x + l)( x 3  -  x 2  + 2).              d) (x – 1 - y)[ ( x   -   1 ) 2   +   ( x   -   1 ) y   +   y 2 ].

x²-x-y²-y=(x²-y²)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)

x²-xy+x-y=x(x-y)+(x-y)=(x+1)(x-y)

\(x^2y^2+2x^2+y^2+2\)

\(=x^2\left(y^2+2\right)+\left(y^2+2\right)\)

\(=\left(x^2+1\right)\left(y^2+2\right)\)

\(a^2-b^2+a-b\)

\(=\left(a+b\right)\left(a-b\right)+\left(a-b\right)\)

\(=\left(a+b+1\right)\left(a-b\right)\)

\(a,x^2y^2+2x^2+y^2+2\)

\(=y^2\left(x^2+1\right)+2\left(x^2+1\right)\)

\(=\left(y^2+2\right)\left(x^2+1\right)\)

\(b,a^2-b^2+a-b\)

\(=\left(a+b\right)\left(a-b\right)+\left(a-b\right)\)

\(=\left(a-b\right)\left(a+b+1\right)\)

a.
=y²(x²+1)+2(x²+1)

=(x²+1)(y²+2)

b.
=(a-b)(a+b)+(a-b)
=(a-b)(a+b+1)

e: \(x^2+6x+9-y^2\)

\(=\left(x+3\right)^2-y^2\)

\(=\left(x+3-y\right)\left(x+3+y\right)\)

f: \(x^2-2x+7x-14\)

\(=x\left(x-2\right)+7\left(x-2\right)\)

=(x-2)(x+7)

h: \(5x^2-10xy+5y^2-20\)

\(=5\left(x^2-2xy+y^2-4\right)\)

\(=5\left(x-y-2\right)\left(x-y+2\right)\)