\(ab\left(x^2+y^2\right)-xy\left(a^2+b^2\right)\)

\(=abx^2+aby^2-a^2xy-b^2xy\)

\(=\left(abx^2-b^2xy\right)-\left(a^2xy-aby^2\right)\)

\(=bx\left(ax-by\right)-ay\left(ax-by\right)\)

\(=\left(ax-by\right)\left(bx-ay\right)\)

x^2 - xy + x - y = x(x - y) + (x - y) = (x - y)(x + 1)

1/(x+2)² -(3x-1)²=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x²+12x

2/(x⁴+x²)(-2x³-2x)=x²(x²+1)-2x(x²+1)=(x²+1)(x²-2x)

x²y-xy²-3x+3y

=(x²y-xy²)-(3x-3y)

=xy(x-y)-3(x-y)

=(x-y).(xy-3)

\(X^2y+xy^2-x-y\)
\(=xy(x+y)-(x+y)=(xy-1)(x+y)\)

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

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

x²-2xy+y²-z²+2zt-t²

=(x²-2xy+y²)-(z²-2zt+t²)              

=(x-y)²-(z-t)²

=(x-y+z-t)(x-y-z+t)   

   x² – 2xy + y² – z² + 2zt – t² = (x² – 2xy + y²) – (z² – 2zt + t²)

= (x – y)² – (z – t)²

= [(x – y) – (z – t)] . [(x – y) + (z – t)]

= (x – y – z + t)(x – y + z – t)

\(x^2-2xy+y^2-z^2+2zt-t^2\)

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

= \(\left(x-y\right)^2-\left(z-t\right)^2\)

=\(\left[\left(x-y\right)+\left(z-t\right)\right]\left[\left(x-y\right)-\left(z-t\right)\right]\)

= \(\left(x-y+z-t\right)\left(x-y-z+t\right)\)

=xy ( x + y ) + z ( x^2 + 2xy + y^2 ) = xy ( x + y ) + z ( x + y ) ^ 2 = ( x + y ) ( xy + xz + yz )

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

em cảm ơn cô @Nguyễn Linh Chi ạ !

1 cách cũng gần giống như cô quản lí 

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

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

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

x(x+y)-5(x+y) = (x-5)(x+y) bài này mik hok qua rùi mik đang ôn tập nên là mik tự làm chứ ko chép mấy câu trả lời khác