a) $25.\left(x-1\right)^2-16\left(x+y\right)^2$

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

= $\left(5x-5-4x-y\right)\left(5x-5+4x+y\right)$

= $\left(x-y-5\right)\left(9x+y-5\right)$

b) $x^3+3x^2+3x+1-27z^3$

= $\left(x+1\right)^3-27z^3$

= $\left(x+1-3z\right)\left(x^2+x.3z+9z^2\right)$

c) $x^2-2xy+y^2-xz+yz$

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

= $\left(x-y\right)\left(x-y-z\right)$

d) $a^3x-ab+b-x$

= $x\left(a^3-1\right)-b\left(a-1\right)$

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

= $\left(a-1\right)\left(a^2x+ax+x-b\right)$

f) $x^2+2x-4y^2-4y$

= $x^2+2x+1-\left(4y^2+4y+1\right)$

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

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

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

g) $xy-4+2x-2y$

= $y\left(x-2\right)-2\left(x-2\right)$

= $\left(x-2\right)\left(y-2\right)$