a: \(x^2-2y-2y^2+x^2y\)
\(=x^2\left(y+1\right)-2y\left(y+1\right)\)
\(=\left(y+1\right)\left(x^2-2y\right)\)
b: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-\left(2xy\right)^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
=(x+y-2xy)(x+y+2xy)
b: \(5x^2y-30xy^2+45y^3\)
\(=5y\left(x^2-6xy+9y^2\right)\)
\(=5y\left(x-3y\right)^2\)
c: \(x^4-4x^2-4x-1\)
\(=\left(x^4-1\right)-4x\left(x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)-4x\left(x+1\right)=\left(x+1\right)\left\lbrack\left(x-1\right)\left(x^2+1\right)-4x\right\rbrack\)
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