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a, = (xy-y^2) + (2x-2y) = y(x-y) + 2.(x-y) = (x-y).(y+2)
b, = (x+y)^2 - 9 = (x+y-3).(x+y+3)
x4 -2x2 +1 =x2.x2 - x2-x2 +1= - x2(1- x2) + (1 - x2)=(1-x2).(1-x2)=(1-x2)2
\(x^4-2x^2+8=x^4+2x^2-4x^2+8=\left(x^2-4\right)\left(x^2+2\right)=\left(x-2\right)\left(x+2\right)\left(x^2+2\right)\)\(\left(x^4-2x^2-8\right):\left(x-2\right)=\left(x+2\right)\left(x^2+2\right)=0\)
\(\Rightarrow x=-2\)
\(3\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)
\(=\left(x^2+x+1\right)\left(3-x^2-x-1\right)\)
\(=\left(x^2+x+1\right)\left(2-x^2-x\right)\)
\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2=3[\left(x^4+2x^2+1\right)-x^2]-\left(x^2+x+1\right)^2\)\(=3[\left(x^2+1\right)^2-x^2]-\left(x^2+x+1\right)^2\)
\(=3\left(x^2-x+1\right)\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)
\(=\left(x^2+x+1\right)\left(2x^2-4x+2\right)=2\left(x-1\right)^2\left(x^2+x+1\right)\)
x ( x2 - 2x + 1 - y)