\(a.\)
\(x^3+2x^2y+xy^2-4x\)
\(=x\left(x^2+2xy+y^2-4\right)\)
\(=x\left[\left(x+y\right)^2-2^2\right]\)
\(=x\left(x+y+2\right)\left(x+y-2\right)\)
\(b.\)
\(x^4+2x^3-4x+4\)
\(=x^4+2x^2+2x^3-4x-2x^2+4\)
\(=x^2\left(x^2+2\right)+2x\left(x^2-2\right)-2\left(x^2+2\right)\)
\(=x^2\left(x^2+2\right)+2x\left(x^2-2\right)-2\left(x^2+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2+2x\right)\)
\(c.\)
\(4x^2-1\)
\(=\left(2x\right)^2-1\)
\(=\left(2x-1\right)\left(2x+1\right)\)
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