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) \(xy-4+2x-2y\)
= \(y\left(x-2\right)-2\left(x-2\right)\)
= \(\left(x-2\right)\left(y-2\right)\)
