a)[tex]x^{4}-4x^{2}+4x-1=x^{4}-1-4x^{2}+4x=\left ( x^{2}-1 \right )\left ( x^{2} +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 [( x-1)\left ( x^{2}+1 \right ) -4\right ]=\left ( x+1 \right )(x^{3}-5)[/tex]
c)[tex]x^{2}\left ( x+4 \right )^{2}-(x+4)^{2}-\left ( x^{2}-1 \right ) =\left ( x^{2}-1 \right )\left ( x+4 \right )^{2}-\left ( x^{2}-1 \right ) =\left ( x^{2}-1 \right )(\left ( x+4 \right )^{2}-1) =\left ( x-1 \right )\left ( x+1 \right )\left ( x +3 \right )\left ( x+5 \right )[/tex]