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\(x^2+y^2-x^2y^2+xy-x-y\)
\(\Leftrightarrow x^2\left(1-y\right)\left(1+y\right)-y\left(1-y\right)-x\left(1-y\right)\)
\(\Leftrightarrow\left(1-y\right)\left(x^2+x^2y-y-x\right)\)
\(\Leftrightarrow\left(1-y\right)\left(x+y\right)\left(x-1\right)\left(x+1\right)\)
\(x^4+y^2-2x^2y+x^2+2x-2y\)
\(=\left(y^2-x^2y-xy\right)-\left(x^2y-x^4-x^3\right)+\left(xy-x^3-x^2\right)-\left(2y-2x^2-2x\right)\)
\(=y\left(y-x^2-x\right)-x^2\left(y-x^2-x\right)+x\left(y-x^2-x\right)-2\left(y-x^2-x\right)\)
\(=\left(y-x^2+x-2\right)\left(y-x^2-x\right)\)
\(a,3x-6y=3\left(x-2y\right)\)
\(b,\frac{2}{5}x^2+5x^3+x^2y=x^2\left(\frac{2}{5}+5x+y\right)\)
\(\frac{12}{5}x^2y^2-9x^4-\frac{4}{25}y^4\)
\(=-\left(\frac{4}{25}y^4-\frac{12}{5}x^2y^2+9x^4\right)\)
\(=-\left[\left(\frac{2}{5}y^2\right)^2-2\cdot\frac{2}{5}y^2\cdot3x^2+\left(3x^2\right)^2\right]\)
\(=-\left(\frac{2}{5}y^2-3x^2\right)^2\)
\(\frac{12}{5}x^2y^2-9x^4-\frac{4}{25}y^4\)
\(=-\left(9x^4-\frac{12}{5}x^2y^2+\frac{4}{25}y^4\right)\)
\(=-\left[\left(3x\right)^2-2.3x^2.\frac{2}{5}y^2+\left(\frac{2}{5}y^2\right)^2\right]\)
\(=-\left(3x^2+\frac{2}{5}y^2\right)\)
x^3-5x2+8x-4=x3-2x2-3x2+6x+2x-4=x2(x-2)-3x(x-2)+2(x-2)
=(x-2)(x2-3x+2)
=(x-2)(x2-2x-x+2)=(x-2)(x-2)(x-1)=(x-2)2(x-1)
A = x^2 + y^2 + 2xy - 2x -2y +1
= (x+y)^2 -2.(x+y) + 1
=(x+y -1 )^2