a) Sửa đề

$x^4+2x^3+x^2$

$=\left(x^4+x^3\right)+\left(x^3+x^2\right)$

$=x^3\left(x+1\right)+x^2\left(x+1\right)$

$=\left(x+1\right)\left(x^3+x^2\right)$

$=\left(x+1\right).x^2\left(x+1\right)$

$=x^2\left(x+1\right)^2$

b) $x^3-x+3x^2y+3xy^2+y^3-y$

$=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)$

$=\left(x+y\right)^3-\left(x+y\right)$

$=\left(x+y\right)\left[\left(x+y\right)^2-1\right]$

$=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)$

c) $5x^2-10xy+5y^2-20z^2$

$=5\left(x^2-2xy+y^2-4z^2\right)$

$=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]$

$=5\left(x-y-2z\right)\left(x-y+2z\right)$